{"id":297766,"date":"2023-12-21T21:16:16","date_gmt":"2023-12-21T14:16:16","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=297766"},"modified":"2026-11-05T09:33:53","modified_gmt":"2026-11-05T02:33:53","slug":"cong-thuc-luong-giac","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-luong-giac\/","title":{"rendered":"B\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 l\u1edbp 10, 11 v\u00e0 m\u1eb9o nh\u1edb nhanh"},"content":{"rendered":"<p><strong>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111\u1eb3ng th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa sin, cos, tan, cot c\u1ee7a m\u1ed9t g\u00f3c (cung), g\u1ed3m 7 nh\u00f3m ch\u00ednh: c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n, c\u00f4ng th\u1ee9c c\u1ed9ng, c\u00f4ng th\u1ee9c nh\u00e2n \u0111\u00f4i v\u00e0 nh\u00e2n ba, c\u00f4ng th\u1ee9c h\u1ea1 b\u1eadc, c\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u1ed5ng th\u00e0nh t\u00edch, bi\u1ebfn \u0111\u1ed5i t\u00edch th\u00e0nh t\u1ed5ng v\u00e0 c\u00f4ng th\u1ee9c c\u00e1c cung li\u00ean quan.<\/strong> \u0110\u00e2y l\u00e0 ki\u1ebfn th\u1ee9c tr\u1ecdng t\u00e2m c\u1ee7a ch\u01b0\u01a1ng l\u01b0\u1ee3ng gi\u00e1c l\u1edbp 10, l\u1edbp 11 v\u00e0 \u0111\u01b0\u1ee3c d\u00f9ng ti\u1ebfp khi h\u1ecdc \u0111\u1ea1o h\u00e0m, t\u00edch ph\u00e2n \u1edf l\u1edbp 12. B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p b\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 d\u01b0\u1edbi d\u1ea1ng b\u1ea3ng tra, c\u00f3 v\u00ed d\u1ee5 gi\u1ea3i m\u1eabu v\u00e0 m\u1eb9o nh\u1edb b\u1eb1ng th\u01a1.<\/p>\n<p><strong>T\u00f3m t\u1eaft nhanh:<\/strong><\/p>\n<ul>\n<li><strong>C\u00f4ng th\u1ee9c g\u1ed1c:<\/strong> sin\u00b2x + cos\u00b2x = 1; tan x = sin x \/ cos x; cot x = cos x \/ sin x; tan x \u00b7 cot x = 1.<\/li>\n<li><strong>C\u00f4ng th\u1ee9c c\u1ed9ng:<\/strong> sin(a \u00b1 b) = sin a cos b \u00b1 cos a sin b; cos(a \u00b1 b) = cos a cos b \u2213 sin a sin b.<\/li>\n<li><strong>Nh\u00e2n \u0111\u00f4i, h\u1ea1 b\u1eadc:<\/strong> sin 2x = 2 sin x cos x; cos 2x = 1 \u2212 2sin\u00b2x; sin\u00b2x = (1 \u2212 cos 2x)\/2.<\/li>\n<li><strong>Cung li\u00ean quan:<\/strong> nh\u1edb c\u00e2u &#8220;cos \u0111\u1ed1i, sin b\u00f9, ph\u1ee5 ch\u00e9o, h\u01a1n k\u00e9m \u03c0 tan cot&#8221;.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><img fetchpriority=\"high\" decoding=\"async\" class=\"alignnone size-full wp-image-298425\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-1.jpg\" alt=\"Tam gi\u00e1c vu\u00f4ng v\u1edbi c\u1ea1nh \u0111\u1ed1i, c\u1ea1nh k\u1ec1, c\u1ea1nh huy\u1ec1n c\u1ee7a g\u00f3c \u03b1 d\u00f9ng \u0111\u1ec3 \u0111\u1ecbnh ngh\u0129a t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>T\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn l\u00e0 g\u00ec?<\/h2>\n<p>Trong tam gi\u00e1c vu\u00f4ng, t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn x l\u00e0 t\u1ec9 s\u1ed1 gi\u1eefa \u0111\u1ed9 d\u00e0i hai c\u1ea1nh c\u1ee7a tam gi\u00e1c. C\u00f3 4 t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n:<\/p>\n<table>\n<thead>\n<tr>\n<th>T\u1ec9 s\u1ed1<\/th>\n<th>\u0110\u1ecbnh ngh\u0129a<\/th>\n<th>M\u1eb9o nh\u1edb<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin x<\/td>\n<td>C\u1ea1nh \u0111\u1ed1i \/ c\u1ea1nh huy\u1ec1n<\/td>\n<td>Sin \u0111i h\u1ecdc<\/td>\n<\/tr>\n<tr>\n<td>cos x<\/td>\n<td>C\u1ea1nh k\u1ec1 \/ c\u1ea1nh huy\u1ec1n<\/td>\n<td>Cos kh\u00f4ng h\u01b0<\/td>\n<\/tr>\n<tr>\n<td>tan x<\/td>\n<td>C\u1ea1nh \u0111\u1ed1i \/ c\u1ea1nh k\u1ec1<\/td>\n<td>Tan \u0111o\u00e0n k\u1ebft<\/td>\n<\/tr>\n<tr>\n<td>cot x<\/td>\n<td>C\u1ea1nh k\u1ec1 \/ c\u1ea1nh \u0111\u1ed1i<\/td>\n<td>Cot k\u1ebft \u0111o\u00e0n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>V\u00ed d\u1ee5: tam gi\u00e1c vu\u00f4ng c\u00f3 c\u1ea1nh \u0111\u1ed1i 3, c\u1ea1nh k\u1ec1 4, c\u1ea1nh huy\u1ec1n 5 th\u00ec sin x = 3\/5, cos x = 4\/5, tan x = 3\/4, cot x = 4\/3. N\u1ebfu b\u1ea1n m\u1edbi l\u00e0m quen v\u1edbi kh\u00e1i ni\u1ec7m, h\u00e3y \u0111\u1ecdc th\u00eam b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/sin-cos-tan-la-gi\/\">sin, cos, tan l\u00e0 g\u00ec<\/a>.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone size-full wp-image-298871\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-11.jpg\" alt=\"V\u00ed d\u1ee5 tam gi\u00e1c vu\u00f4ng c\u1ea1nh 3, 4, 5 v\u00e0 c\u00e1ch t\u00ednh sin, cos, tan c\u1ee7a g\u00f3c \u03b8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-11.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-11-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-11-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u1ea3ng gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a c\u00e1c g\u00f3c \u0111\u1eb7c bi\u1ec7t<\/h2>\n<p>\u0110\u00e2y l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb c\u1ea7n thu\u1ed9c l\u00f2ng v\u00ec xu\u1ea5t hi\u1ec7n trong h\u1ea7u h\u1ebft b\u00e0i t\u1eadp.<\/p>\n<table>\n<thead>\n<tr>\n<th>G\u00f3c<\/th>\n<th>0\u00b0<\/th>\n<th>30\u00b0 (\u03c0\/6)<\/th>\n<th>45\u00b0 (\u03c0\/4)<\/th>\n<th>60\u00b0 (\u03c0\/3)<\/th>\n<th>90\u00b0 (\u03c0\/2)<\/th>\n<th>180\u00b0 (\u03c0)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin<\/td>\n<td>0<\/td>\n<td>1\/2<\/td>\n<td>\u221a2\/2<\/td>\n<td>\u221a3\/2<\/td>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>cos<\/td>\n<td>1<\/td>\n<td>\u221a3\/2<\/td>\n<td>\u221a2\/2<\/td>\n<td>1\/2<\/td>\n<td>0<\/td>\n<td>\u22121<\/td>\n<\/tr>\n<tr>\n<td>tan<\/td>\n<td>0<\/td>\n<td>\u221a3\/3<\/td>\n<td>1<\/td>\n<td>\u221a3<\/td>\n<td>Kh\u00f4ng x\u00e1c \u0111\u1ecbnh<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>cot<\/td>\n<td>Kh\u00f4ng x\u00e1c \u0111\u1ecbnh<\/td>\n<td>\u221a3<\/td>\n<td>1<\/td>\n<td>\u221a3\/3<\/td>\n<td>0<\/td>\n<td>Kh\u00f4ng x\u00e1c \u0111\u1ecbnh<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>B\u1ea3ng \u0111\u1ea7y \u0111\u1ee7 v\u1edbi nhi\u1ec1u g\u00f3c h\u01a1n c\u00f3 trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/bang-gia-tri-luong-giac\/\">b\u1ea3ng gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c<\/a>.<\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" class=\"alignnone size-full wp-image-298879\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-17.jpg\" alt=\"\u0110\u01b0\u1eddng tr\u00f2n l\u01b0\u1ee3ng gi\u00e1c b\u00e1n k\u00ednh 1 v\u1edbi cos \u03b8 tr\u00ean tr\u1ee5c ho\u00e0nh v\u00e0 sin \u03b8 tr\u00ean tr\u1ee5c tung\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-17.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-17-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-17-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n<\/h2>\n<table>\n<thead>\n<tr>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<th>\u0110i\u1ec1u ki\u1ec7n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin\u00b2x + cos\u00b2x = 1<\/td>\n<td>M\u1ecdi x<\/td>\n<\/tr>\n<tr>\n<td>tan x = sin x \/ cos x<\/td>\n<td>cos x \u2260 0<\/td>\n<\/tr>\n<tr>\n<td>cot x = cos x \/ sin x<\/td>\n<td>sin x \u2260 0<\/td>\n<\/tr>\n<tr>\n<td>tan x \u00b7 cot x = 1<\/td>\n<td>sin x \u2260 0, cos x \u2260 0<\/td>\n<\/tr>\n<tr>\n<td>1 + tan\u00b2x = 1 \/ cos\u00b2x<\/td>\n<td>cos x \u2260 0<\/td>\n<\/tr>\n<tr>\n<td>1 + cot\u00b2x = 1 \/ sin\u00b2x<\/td>\n<td>sin x \u2260 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Gi\u00e1 tr\u1ecb c\u1ee7a sin v\u00e0 cos lu\u00f4n n\u1eb1m trong \u0111o\u1ea1n [\u22121; 1], c\u00f2n tan v\u00e0 cot c\u00f3 th\u1ec3 nh\u1eadn m\u1ecdi gi\u00e1 tr\u1ecb th\u1ef1c.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298426\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-2.jpg\" alt=\"B\u00e0i t\u1eadp ch\u1ee9ng minh c\u00f4ng th\u1ee9c tan b\u1eb1ng sin chia cos v\u00e0 sin b\u00ecnh c\u1ed9ng cos b\u00ecnh b\u1eb1ng 1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c c\u1ed9ng l\u01b0\u1ee3ng gi\u00e1c<\/h2>\n<table>\n<thead>\n<tr>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin(a + b) = sin a \u00b7 cos b + cos a \u00b7 sin b<\/td>\n<\/tr>\n<tr>\n<td>sin(a \u2212 b) = sin a \u00b7 cos b \u2212 cos a \u00b7 sin b<\/td>\n<\/tr>\n<tr>\n<td>cos(a + b) = cos a \u00b7 cos b \u2212 sin a \u00b7 sin b<\/td>\n<\/tr>\n<tr>\n<td>cos(a \u2212 b) = cos a \u00b7 cos b + sin a \u00b7 sin b<\/td>\n<\/tr>\n<tr>\n<td>tan(a + b) = (tan a + tan b) \/ (1 \u2212 tan a \u00b7 tan b)<\/td>\n<\/tr>\n<tr>\n<td>tan(a \u2212 b) = (tan a \u2212 tan b) \/ (1 + tan a \u00b7 tan b)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>L\u01b0u \u00fd d\u1ea5u: v\u1edbi cos, d\u1ea5u \u1edf v\u1ebf ph\u1ea3i <strong>ng\u01b0\u1ee3c<\/strong> v\u1edbi d\u1ea5u \u1edf v\u1ebf tr\u00e1i; v\u1edbi sin, d\u1ea5u gi\u1eef nguy\u00ean.<\/p>\n<h2>C\u00f4ng th\u1ee9c nh\u00e2n \u0111\u00f4i v\u00e0 nh\u00e2n ba<\/h2>\n<table>\n<thead>\n<tr>\n<th>Nh\u00f3m<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td rowspan=\"3\">Nh\u00e2n \u0111\u00f4i<\/td>\n<td>sin 2x = 2 sin x \u00b7 cos x<\/td>\n<\/tr>\n<tr>\n<td>cos 2x = cos\u00b2x \u2212 sin\u00b2x = 2cos\u00b2x \u2212 1 = 1 \u2212 2sin\u00b2x<\/td>\n<\/tr>\n<tr>\n<td>tan 2x = 2 tan x \/ (1 \u2212 tan\u00b2x)<\/td>\n<\/tr>\n<tr>\n<td rowspan=\"3\">Nh\u00e2n ba<\/td>\n<td>sin 3x = 3 sin x \u2212 4 sin\u00b3x<\/td>\n<\/tr>\n<tr>\n<td>cos 3x = 4 cos\u00b3x \u2212 3 cos x<\/td>\n<\/tr>\n<tr>\n<td>tan 3x = (3 tan x \u2212 tan\u00b3x) \/ (1 \u2212 3tan\u00b2x)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298882\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-20.jpg\" alt=\"\u0110\u1ed3 th\u1ecb y = cos x, y = cos 2x v\u00e0 y = cos 4x minh h\u1ecda chu k\u1ef3 thay \u0111\u1ed5i khi nh\u00e2n g\u00f3c\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-20.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-20-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-20-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c h\u1ea1 b\u1eadc<\/h2>\n<p>C\u00f4ng th\u1ee9c h\u1ea1 b\u1eadc d\u00f9ng \u0111\u1ec3 \u0111\u01b0a sin\u00b2, cos\u00b2 v\u1ec1 b\u1eadc nh\u1ea5t c\u1ee7a g\u00f3c nh\u00e2n \u0111\u00f4i, r\u1ea5t hay d\u00f9ng khi gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 t\u00ednh t\u00edch ph\u00e2n.<\/p>\n<table>\n<thead>\n<tr>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin\u00b2x = (1 \u2212 cos 2x) \/ 2<\/td>\n<\/tr>\n<tr>\n<td>cos\u00b2x = (1 + cos 2x) \/ 2<\/td>\n<\/tr>\n<tr>\n<td>tan\u00b2x = (1 \u2212 cos 2x) \/ (1 + cos 2x)<\/td>\n<\/tr>\n<tr>\n<td>sin\u00b3x = (3 sin x \u2212 sin 3x) \/ 4<\/td>\n<\/tr>\n<tr>\n<td>cos\u00b3x = (3 cos x + cos 3x) \/ 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u1ed5ng th\u00e0nh t\u00edch<\/h2>\n<table>\n<thead>\n<tr>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>cos a + cos b = 2 cos((a + b)\/2) \u00b7 cos((a \u2212 b)\/2)<\/td>\n<\/tr>\n<tr>\n<td>cos a \u2212 cos b = \u22122 sin((a + b)\/2) \u00b7 sin((a \u2212 b)\/2)<\/td>\n<\/tr>\n<tr>\n<td>sin a + sin b = 2 sin((a + b)\/2) \u00b7 cos((a \u2212 b)\/2)<\/td>\n<\/tr>\n<tr>\n<td>sin a \u2212 sin b = 2 cos((a + b)\/2) \u00b7 sin((a \u2212 b)\/2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u00edch th\u00e0nh t\u1ed5ng<\/h2>\n<table>\n<thead>\n<tr>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>cos a \u00b7 cos b = \u00bd[cos(a + b) + cos(a \u2212 b)]<\/td>\n<\/tr>\n<tr>\n<td>sin a \u00b7 sin b = \u00bd[cos(a \u2212 b) \u2212 cos(a + b)]<\/td>\n<\/tr>\n<tr>\n<td>sin a \u00b7 cos b = \u00bd[sin(a + b) + sin(a \u2212 b)]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298873\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-13.jpg\" alt=\"B\u1ea3ng ph\u1ea5n v\u1edbi h\u00ecnh h\u1ecdc, c\u00f4ng th\u1ee9c sin cos v\u00e0 \u0111\u1ecbnh l\u00fd Pytago\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-13.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-13-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-13-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a c\u00e1c cung li\u00ean quan<\/h2>\n<p>C\u00e1c c\u00f4ng th\u1ee9c d\u01b0\u1edbi \u0111\u00e2y gi\u00fap \u0111\u01b0a gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a m\u1ed9t g\u00f3c b\u1ea5t k\u1ef3 v\u1ec1 g\u00f3c nh\u1ecdn quen thu\u1ed9c.<\/p>\n<table>\n<thead>\n<tr>\n<th>Quan h\u1ec7<\/th>\n<th>sin<\/th>\n<th>cos<\/th>\n<th>tan<\/th>\n<th>cot<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Cung \u0111\u1ed1i nhau (x v\u00e0 \u2212x)<\/td>\n<td>sin(\u2212x) = \u2212sin x<\/td>\n<td>cos(\u2212x) = cos x<\/td>\n<td>tan(\u2212x) = \u2212tan x<\/td>\n<td>cot(\u2212x) = \u2212cot x<\/td>\n<\/tr>\n<tr>\n<td>Cung b\u00f9 nhau (x v\u00e0 \u03c0 \u2212 x)<\/td>\n<td>sin(\u03c0 \u2212 x) = sin x<\/td>\n<td>cos(\u03c0 \u2212 x) = \u2212cos x<\/td>\n<td>tan(\u03c0 \u2212 x) = \u2212tan x<\/td>\n<td>cot(\u03c0 \u2212 x) = \u2212cot x<\/td>\n<\/tr>\n<tr>\n<td>Cung ph\u1ee5 nhau (x v\u00e0 \u03c0\/2 \u2212 x)<\/td>\n<td>sin(\u03c0\/2 \u2212 x) = cos x<\/td>\n<td>cos(\u03c0\/2 \u2212 x) = sin x<\/td>\n<td>tan(\u03c0\/2 \u2212 x) = cot x<\/td>\n<td>cot(\u03c0\/2 \u2212 x) = tan x<\/td>\n<\/tr>\n<tr>\n<td>H\u01a1n k\u00e9m \u03c0 (x v\u00e0 \u03c0 + x)<\/td>\n<td>sin(\u03c0 + x) = \u2212sin x<\/td>\n<td>cos(\u03c0 + x) = \u2212cos x<\/td>\n<td>tan(\u03c0 + x) = tan x<\/td>\n<td>cot(\u03c0 + x) = cot x<\/td>\n<\/tr>\n<tr>\n<td>H\u01a1n k\u00e9m \u03c0\/2 (x v\u00e0 \u03c0\/2 + x)<\/td>\n<td>sin(\u03c0\/2 + x) = cos x<\/td>\n<td>cos(\u03c0\/2 + x) = \u2212sin x<\/td>\n<td>tan(\u03c0\/2 + x) = \u2212cot x<\/td>\n<td>cot(\u03c0\/2 + x) = \u2212tan x<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>V\u00ed d\u1ee5: sin 150\u00b0 = sin(180\u00b0 \u2212 30\u00b0) = sin 30\u00b0 = 1\/2; cos 120\u00b0 = cos(180\u00b0 \u2212 60\u00b0) = \u2212cos 60\u00b0 = \u22121\/2; tan 210\u00b0 = tan(180\u00b0 + 30\u00b0) = tan 30\u00b0 = \u221a3\/3.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298430\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-6.jpg\" alt=\"\u0110\u01b0\u1eddng tr\u00f2n l\u01b0\u1ee3ng gi\u00e1c \u0111\u00e1nh d\u1ea5u c\u00e1c cung \u0111\u1eb7c bi\u1ec7t d\u00f9ng trong b\u00e0i t\u1eadp\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c t\u00ednh theo t = tan(x\/2)<\/h2>\n<p>Khi \u0111\u1eb7t t = tan(x\/2) (v\u1edbi cos(x\/2) \u2260 0), c\u00f3 th\u1ec3 bi\u1ec3u di\u1ec5n sin x, cos x, tan x theo t. C\u00e1ch \u0111\u1eb7t n\u00e0y hay d\u00f9ng \u0111\u1ec3 \u0111\u01b0a ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng \u0111\u1ea1i s\u1ed1:<\/p>\n<ul>\n<li>sin x = 2t \/ (1 + t\u00b2)<\/li>\n<li>cos x = (1 \u2212 t\u00b2) \/ (1 + t\u00b2)<\/li>\n<li>tan x = 2t \/ (1 \u2212 t\u00b2), v\u1edbi t\u00b2 \u2260 1<\/li>\n<\/ul>\n<h2>C\u00f4ng th\u1ee9c nghi\u1ec7m ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n<\/h2>\n<table>\n<thead>\n<tr>\n<th>Ph\u01b0\u01a1ng tr\u00ecnh<\/th>\n<th>Nghi\u1ec7m (k \u2208 \u2124)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>sin x = sin a<\/td>\n<td>x = a + k2\u03c0 ho\u1eb7c x = \u03c0 \u2212 a + k2\u03c0<\/td>\n<\/tr>\n<tr>\n<td>cos x = cos a<\/td>\n<td>x = a + k2\u03c0 ho\u1eb7c x = \u2212a + k2\u03c0<\/td>\n<\/tr>\n<tr>\n<td>tan x = tan a<\/td>\n<td>x = a + k\u03c0<\/td>\n<\/tr>\n<tr>\n<td>cot x = cot a<\/td>\n<td>x = a + k\u03c0<\/td>\n<\/tr>\n<tr>\n<td>sin x = 0; sin x = 1; sin x = \u22121<\/td>\n<td>x = k\u03c0; x = \u03c0\/2 + k2\u03c0; x = \u2212\u03c0\/2 + k2\u03c0<\/td>\n<\/tr>\n<tr>\n<td>cos x = 0; cos x = 1; cos x = \u22121<\/td>\n<td>x = \u03c0\/2 + k\u03c0; x = k2\u03c0; x = \u03c0 + k2\u03c0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>C\u00e1ch gi\u1ea3i t\u1eebng d\u1ea1ng v\u00e0 v\u00ed d\u1ee5 chi ti\u1ebft c\u00f3 trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-luong-giac\/\">ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n<\/a>.<\/p>\n<h2>V\u00ed d\u1ee5 \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p><strong>V\u00ed d\u1ee5 1:<\/strong> T\u00ednh cos 75\u00b0.<\/p>\n<ul>\n<li>cos 75\u00b0 = cos(45\u00b0 + 30\u00b0) = cos 45\u00b0 cos 30\u00b0 \u2212 sin 45\u00b0 sin 30\u00b0 = (\u221a2\/2)(\u221a3\/2) \u2212 (\u221a2\/2)(1\/2) = <strong>(\u221a6 \u2212 \u221a2)\/4 \u2248 0,2588<\/strong>.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 2:<\/strong> T\u00ednh tan 15\u00b0.<\/p>\n<ul>\n<li>tan 15\u00b0 = tan(45\u00b0 \u2212 30\u00b0) = (1 \u2212 \u221a3\/3) \/ (1 + \u221a3\/3) = (3 \u2212 \u221a3) \/ (3 + \u221a3) = <strong>2 \u2212 \u221a3 \u2248 0,2679<\/strong>.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 3:<\/strong> Cho sin x = 3\/5 v\u1edbi 0 &lt; x &lt; \u03c0\/2. T\u00ednh cos x, sin 2x, cos 2x.<\/p>\n<ul>\n<li>cos\u00b2x = 1 \u2212 9\/25 = 16\/25, x thu\u1ed9c g\u00f3c ph\u1ea7n t\u01b0 th\u1ee9 nh\u1ea5t n\u00ean cos x = <strong>4\/5<\/strong>.<\/li>\n<li>sin 2x = 2 \u00b7 (3\/5) \u00b7 (4\/5) = <strong>24\/25<\/strong>.<\/li>\n<li>cos 2x = 1 \u2212 2 \u00b7 (9\/25) = <strong>7\/25<\/strong>.<\/li>\n<\/ul>\n<p><strong>V\u00ed d\u1ee5 4:<\/strong> R\u00fat g\u1ecdn A = sin(\u03c0 \u2212 x) + cos(\u03c0\/2 \u2212 x) + sin(\u03c0 + x).<\/p>\n<ul>\n<li>A = sin x + sin x \u2212 sin x = <strong>sin x<\/strong>.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298428\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-4.jpg\" alt=\"\u0110\u1ec1 ki\u1ec3m tra l\u01b0\u1ee3ng gi\u00e1c v\u1edbi b\u00e0i t\u1eadp t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c v\u00e0 gi\u1ea3i tam gi\u00e1c vu\u00f4ng\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>M\u1eb9o ghi nh\u1edb c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c b\u1eb1ng th\u01a1<\/h2>\n<p><strong>T\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c:<\/strong> &#8220;Sin \u0111i h\u1ecdc, Cos kh\u00f4ng h\u01b0, Tan \u0111o\u00e0n k\u1ebft, Cot k\u1ebft \u0111o\u00e0n&#8221; (sin = \u0111\u1ed1i\/huy\u1ec1n, cos = k\u1ec1\/huy\u1ec1n, tan = \u0111\u1ed1i\/k\u1ec1, cot = k\u1ec1\/\u0111\u1ed1i).<\/p>\n<p><strong>C\u00f4ng th\u1ee9c c\u1ed9ng:<\/strong><\/p>\n<p>&#8220;Sin th\u00ec sin cos cos sin<br \/>Cos th\u00ec cos cos sin sin d\u1ea5u tr\u1eeb<br \/>Tan t\u1ed5ng th\u00ec l\u1ea5y t\u1ed5ng tan<br \/>Chia m\u1ed9t tr\u1eeb v\u1edbi t\u00edch tan, d\u1ec5 m\u00e0.&#8221;<\/p>\n<p><strong>Cung li\u00ean quan:<\/strong> &#8220;Cos \u0111\u1ed1i, sin b\u00f9, ph\u1ee5 ch\u00e9o, h\u01a1n k\u00e9m \u03c0 tan cot&#8221;: hai cung \u0111\u1ed1i c\u00f3 cos b\u1eb1ng nhau, hai cung b\u00f9 c\u00f3 sin b\u1eb1ng nhau, hai cung ph\u1ee5 th\u00ec sin cung n\u00e0y b\u1eb1ng cos cung kia, hai cung h\u01a1n k\u00e9m \u03c0 c\u00f3 tan v\u00e0 cot b\u1eb1ng nhau.<\/p>\n<p><strong>T\u1ed5ng th\u00e0nh t\u00edch:<\/strong><\/p>\n<p>&#8220;Cos c\u1ed9ng cos b\u1eb1ng hai cos cos<br \/>Cos tr\u1eeb cos b\u1eb1ng tr\u1eeb hai sin sin<br \/>Sin c\u1ed9ng sin b\u1eb1ng hai sin cos<br \/>Sin tr\u1eeb sin b\u1eb1ng hai cos sin.&#8221;<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298878\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-16.jpg\" alt=\"N\u1ec1n b\u1ea3ng \u0111en chi ch\u00edt c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c vi\u1ebft tay\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-16.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-16-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-16-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a l\u01b0\u1ee3ng gi\u00e1c trong th\u1ef1c t\u1ebf<\/h2>\n<ul>\n<li><strong>\u0110o \u0111\u1ea1c:<\/strong> t\u00ednh chi\u1ec1u cao t\u00f2a nh\u00e0, \u0111\u1ed9 s\u00e2u, kho\u1ea3ng c\u00e1ch khi bi\u1ebft m\u1ed9t c\u1ea1nh v\u00e0 g\u00f3c nh\u00ecn.<\/li>\n<li><strong>V\u1eadt l\u00fd:<\/strong> m\u00f4 t\u1ea3 dao \u0111\u1ed9ng \u0111i\u1ec1u h\u00f2a, s\u00f3ng, d\u00f2ng \u0111i\u1ec7n xoay chi\u1ec1u b\u1eb1ng h\u00e0m sin, cos.<\/li>\n<li><strong>K\u1ef9 thu\u1eadt, x\u00e2y d\u1ef1ng:<\/strong> t\u00ednh l\u1ef1c, \u0111\u1ed9 d\u1ed1c, g\u00f3c nghi\u00eang c\u1ee7a k\u1ebft c\u1ea5u.<\/li>\n<li><strong>H\u00e0ng kh\u00f4ng, h\u00e0ng h\u1ea3i:<\/strong> x\u00e1c \u0111\u1ecbnh g\u00f3c c\u1ea5t c\u00e1nh, h\u01b0\u1edbng \u0111i, \u0111\u1ecbnh v\u1ecb.<\/li>\n<li><strong>C\u00f4ng ngh\u1ec7:<\/strong> x\u1eed l\u00fd t\u00edn hi\u1ec7u s\u1ed1, n\u00e9n \u1ea3nh, \u0111\u1ed3 h\u1ecda m\u00e1y t\u00ednh.<\/li>\n<\/ul>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298875\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-15.jpg\" alt=\"B\u00e0i to\u00e1n t\u00e0u ng\u1ea7m d\u00f9ng t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c v\u1edbi c\u1ea1nh k\u1ec1 550 m v\u00e0 c\u1ea1nh huy\u1ec1n 650 m\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-15.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-15-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-15-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298874\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-14.jpg\" alt=\"B\u00e0i to\u00e1n m\u00e1y bay c\u1ea5t c\u00e1nh t\u00ednh g\u00f3c \u03b8 t\u1eeb qu\u00e3ng \u0111\u01b0\u1eddng 100.000 ft v\u00e0 \u0111\u1ed9 cao 40.000 ft\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-14.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-14-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-14-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<p>V\u00ed d\u1ee5 v\u1edbi h\u00ecnh m\u00e1y bay: sin \u03b8 = 40.000 \/ 100.000 = 0,4 n\u00ean \u03b8 \u2248 23,6\u00b0. Trong tam gi\u00e1c th\u01b0\u1eddng, b\u1ea1n d\u00f9ng th\u00eam <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dinh-ly-cosin\/\">\u0111\u1ecbnh l\u00fd cosin<\/a> \u0111\u1ec3 t\u00ednh c\u1ea1nh v\u00e0 g\u00f3c.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-298880\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-18.jpg\" alt=\"K\u1ef9 s\u01b0 l\u1eafp \u0111\u1eb7t thi\u1ebft b\u1ecb \u0111i\u1ec7n, l\u0129nh v\u1ef1c \u1ee9ng d\u1ee5ng h\u00e0m l\u01b0\u1ee3ng gi\u00e1c trong d\u00f2ng \u0111i\u1ec7n xoay chi\u1ec1u\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-18.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-18-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-luong-giac-18-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>L\u01b0u \u00fd khi s\u1eed d\u1ee5ng b\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c<\/h2>\n<ul>\n<li><strong>\u0110\u01a1n v\u1ecb g\u00f3c:<\/strong> c\u00e1c c\u00f4ng th\u1ee9c nghi\u1ec7m vi\u1ebft theo radian (\u03c0), kh\u00f4ng tr\u1ed9n \u0111\u1ed9 v\u00e0 radian trong c\u00f9ng m\u1ed9t nghi\u1ec7m.<\/li>\n<li><strong>\u0110i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh:<\/strong> tan c\u1ea7n cos x \u2260 0, cot c\u1ea7n sin x \u2260 0; lu\u00f4n ki\u1ec3m tra tr\u01b0\u1edbc khi bi\u1ebfn \u0111\u1ed5i.<\/li>\n<li><strong>D\u1ea5u theo g\u00f3c ph\u1ea7n t\u01b0:<\/strong> khi suy cos t\u1eeb sin (ho\u1eb7c ng\u01b0\u1ee3c l\u1ea1i) ph\u1ea3i x\u00e9t g\u00f3c thu\u1ed9c g\u00f3c ph\u1ea7n t\u01b0 n\u00e0o \u0111\u1ec3 ch\u1ecdn d\u1ea5u.<\/li>\n<li><strong>Ki\u1ec3m tra b\u1eb1ng m\u00e1y t\u00ednh:<\/strong> thay m\u1ed9t gi\u00e1 tr\u1ecb g\u00f3c c\u1ee5 th\u1ec3 v\u00e0o hai v\u1ebf \u0111\u1ec3 ki\u1ec3m tra c\u00f4ng th\u1ee9c v\u1eeba bi\u1ebfn \u0111\u1ed5i.<\/li>\n<\/ul>\n<p>V\u1edbi d\u1ea1ng b\u00e0i kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c, b\u1ea1n c\u00f3 th\u1ec3 \u00f4n th\u00eam <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tinh-don-dieu-cua-ham-so\/\">t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/a>. \u1ede ph\u1ea7n h\u00ecnh h\u1ecdc, c\u00e1c h\u1ec7 th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u0169ng hay d\u00f9ng khi ch\u1ee9ng minh <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dau-hieu-nhan-biet-tu-giac-noi-tiep\/\">t\u1ee9 gi\u00e1c n\u1ed9i ti\u1ebfp<\/a>.<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c<\/h2>\n<h3>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n nh\u1ea5t l\u00e0 g\u00ec?<\/h3>\n<p>C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n nh\u1ea5t l\u00e0 sin\u00b2x + cos\u00b2x = 1, k\u00e8m theo tan x = sin x \/ cos x v\u00e0 cot x = cos x \/ sin x.<\/p>\n<h3>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c h\u1ecdc \u1edf l\u1edbp m\u1ea5y?<\/h3>\n<p>Theo ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi, t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn h\u1ecdc \u1edf l\u1edbp 9, gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0 h\u1ecdc \u1edf l\u1edbp 10, c\u00f2n c\u00e1c c\u00f4ng th\u1ee9c c\u1ed9ng, nh\u00e2n \u0111\u00f4i, bi\u1ebfn \u0111\u1ed5i v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c h\u1ecdc \u1edf l\u1edbp 11.<\/p>\n<h3>C\u00f4ng th\u1ee9c nh\u00e2n \u0111\u00f4i c\u1ee7a cos l\u00e0 g\u00ec?<\/h3>\n<p>cos 2x = cos\u00b2x \u2212 sin\u00b2x = 2cos\u00b2x \u2212 1 = 1 \u2212 2sin\u00b2x.<\/p>\n<h3>C\u00e1ch nh\u1edb c\u00f4ng th\u1ee9c cung li\u00ean quan nhanh nh\u1ea5t?<\/h3>\n<p>Nh\u1edb c\u00e2u &#8220;cos \u0111\u1ed1i, sin b\u00f9, ph\u1ee5 ch\u00e9o, h\u01a1n k\u00e9m \u03c0 tan cot&#8221;, r\u1ed3i suy ra d\u1ea5u c\u1ee7a c\u00e1c h\u00e0m c\u00f2n l\u1ea1i theo g\u00f3c ph\u1ea7n t\u01b0.<\/p>\n<h3>tan(\u03c0 \u2212 x) b\u1eb1ng bao nhi\u00eau?<\/h3>\n<p>tan(\u03c0 \u2212 x) = \u2212tan x, v\u00ec hai cung b\u00f9 nhau c\u00f3 sin b\u1eb1ng nhau c\u00f2n cos \u0111\u1ed1i nhau.<\/p>\n<h3>C\u00f3 c\u1ea7n h\u1ecdc thu\u1ed9c c\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u00edch th\u00e0nh t\u1ed5ng kh\u00f4ng?<\/h3>\n<p>N\u00ean nh\u1edb, nh\u01b0ng c\u00f3 th\u1ec3 t\u1ef1 suy ra nhanh b\u1eb1ng c\u00e1ch c\u1ed9ng ho\u1eb7c tr\u1eeb hai c\u00f4ng th\u1ee9c c\u1ed9ng, v\u00ed d\u1ee5 c\u1ed9ng cos(a + b) v\u00e0 cos(a \u2212 b) \u0111\u01b0\u1ee3c 2cos a cos b.<\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n nh\u1ea5t l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"C\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n nh\u1ea5t l\u00e0 sin\u00b2x + cos\u00b2x = 1, k\u00e8m theo tan x = sin x \/ cos x v\u00e0 cot x = cos x \/ sin x.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c h\u1ecdc \u1edf l\u1edbp m\u1ea5y?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Theo ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi, t\u1ec9 s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c nh\u1ecdn h\u1ecdc \u1edf l\u1edbp 9, gi\u00e1 tr\u1ecb l\u01b0\u1ee3ng gi\u00e1c c\u1ee7a g\u00f3c t\u1eeb 0\u00b0 \u0111\u1ebfn 180\u00b0 h\u1ecdc \u1edf l\u1edbp 10, c\u00f2n c\u00e1c c\u00f4ng th\u1ee9c c\u1ed9ng, nh\u00e2n \u0111\u00f4i, bi\u1ebfn \u0111\u1ed5i v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh l\u01b0\u1ee3ng gi\u00e1c h\u1ecdc \u1edf l\u1edbp 11.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c nh\u00e2n \u0111\u00f4i c\u1ee7a cos l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"cos 2x = cos\u00b2x \u2212 sin\u00b2x = 2cos\u00b2x \u2212 1 = 1 \u2212 2sin\u00b2x.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00e1ch nh\u1edb c\u00f4ng th\u1ee9c cung li\u00ean quan nhanh nh\u1ea5t?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"Nh\u1edb c\u00e2u \\\"cos \u0111\u1ed1i, sin b\u00f9, ph\u1ee5 ch\u00e9o, h\u01a1n k\u00e9m \u03c0 tan cot\\\", r\u1ed3i suy ra d\u1ea5u c\u1ee7a c\u00e1c h\u00e0m c\u00f2n l\u1ea1i theo g\u00f3c ph\u1ea7n t\u01b0.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"tan(\u03c0 \u2212 x) b\u1eb1ng bao nhi\u00eau?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"tan(\u03c0 \u2212 x) = \u2212tan x, v\u00ec hai cung b\u00f9 nhau c\u00f3 sin b\u1eb1ng nhau c\u00f2n cos \u0111\u1ed1i nhau.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f3 c\u1ea7n h\u1ecdc thu\u1ed9c c\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u00edch th\u00e0nh t\u1ed5ng kh\u00f4ng?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"N\u00ean nh\u1edb, nh\u01b0ng c\u00f3 th\u1ec3 t\u1ef1 suy ra nhanh b\u1eb1ng c\u00e1ch c\u1ed9ng ho\u1eb7c tr\u1eeb hai c\u00f4ng th\u1ee9c c\u1ed9ng, v\u00ed d\u1ee5 c\u1ed9ng cos(a + b) v\u00e0 cos(a \u2212 b) \u0111\u01b0\u1ee3c 2cos a cos b.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>B\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c g\u1ed3m c\u00e1c nh\u00f3m c\u01a1 b\u1ea3n, c\u1ed9ng, nh\u00e2n \u0111\u00f4i, nh\u00e2n ba, h\u1ea1 b\u1eadc, bi\u1ebfn \u0111\u1ed5i t\u1ed5ng \u2013 t\u00edch v\u00e0 cung li\u00ean quan. H\u00e3y n\u1eafm ch\u1eafc c\u00f4ng th\u1ee9c g\u1ed1c sin\u00b2x + cos\u00b2x = 1 v\u00e0 c\u00f4ng th\u1ee9c c\u1ed9ng, v\u00ec ph\u1ea7n l\u1edbn c\u00f4ng th\u1ee9c c\u00f2n l\u1ea1i \u0111\u1ec1u suy ra t\u1eeb \u0111\u00e2y. K\u1ebft h\u1ee3p b\u1ea3ng gi\u00e1 tr\u1ecb g\u00f3c \u0111\u1eb7c bi\u1ec7t, m\u1eb9o nh\u1edb b\u1eb1ng th\u01a1 v\u00e0 luy\u1ec7n c\u00e1c v\u00ed d\u1ee5 trong b\u00e0i, b\u1ea1n s\u1ebd gi\u1ea3i nhanh c\u00e1c d\u1ea1ng b\u00e0i l\u01b0\u1ee3ng gi\u00e1c t\u1eeb l\u1edbp 10 \u0111\u1ebfn l\u1edbp 12.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111\u1eb3ng th\u1ee9c li\u00ean h\u1ec7 gi\u1eefa sin, cos, tan, cot c\u1ee7a m\u1ed9t g\u00f3c (cung), g\u1ed3m 7 nh\u00f3m ch\u00ednh: c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n, c\u00f4ng th\u1ee9c c\u1ed9ng, c\u00f4ng th\u1ee9c nh\u00e2n \u0111\u00f4i v\u00e0 nh\u00e2n ba, c\u00f4ng th\u1ee9c h\u1ea1 b\u1eadc, c\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i t\u1ed5ng th\u00e0nh t\u00edch, bi\u1ebfn \u0111\u1ed5i t\u00edch th\u00e0nh t\u1ed5ng [&hellip;]<\/p>\n","protected":false},"author":75,"featured_media":298431,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c","_yoast_wpseo_title":"B\u1ea3ng C\u00f4ng Th\u1ee9c L\u01b0\u1ee3ng Gi\u00e1c \u0110\u1ea7y \u0110\u1ee7 (A-Z) & M\u1eb9o Nh\u1edb D\u1ec5 Thu\u1ed9c","_yoast_wpseo_metadesc":"B\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7 l\u1edbp 10, 11: c\u00f4ng th\u1ee9c c\u1ed9ng, nh\u00e2n \u0111\u00f4i, h\u1ea1 b\u1eadc, bi\u1ebfn \u0111\u1ed5i, cung li\u00ean quan k\u00e8m v\u00ed d\u1ee5 gi\u1ea3i m\u1eabu v\u00e0 m\u1eb9o nh\u1edb b\u1eb1ng th\u01a1.","footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-297766","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO 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