2cosx等于多少公式？ cos²x可以用什么公式
2cosx\u7b49\u4e8e\u591a\u5c11\u516c\u5f0fcos2x=1-2sinx^2\uff0ccos2x=2cosx^2-1\uff1b
\u8fd9\u516c\u5f0f\u662f\u8fd9\u6837\u63a8\u5bfc\u51fa\u6765\u7684\uff1b
cos2x
=cos\uff08x+x\uff09
=cosx*cosx-sinx*sinx
=cosx^2-sinx^2
=cosx^2-\uff081-cosx^2\uff09
=2cosx^2-1
cosx^2-sinx^2
=\uff081-sinx^2\uff09-sinx^2
=1-2sinx^2
\u89e3\uff1a
cos2x\uff1dcos²x\uff0dsin²x
\uff1d2cos²x\uff0d1
\uff1d1\uff0d2sin²x
\uff1d\uff081\uff0dtan²x\uff09\uff0f\uff081\uff0btan²x\uff09
k\u00d7\u03c0\uff0f2\u00b1a\uff08k\u2208z\uff09\u7684\u4e09\u89d2\u51fd\u6570\u503c\u3002
\u5f53k\u4e3a\u5076\u6570\u65f6\uff0c\u7b49\u4e8e\u03b1\u7684\u540c\u540d\u4e09\u89d2\u51fd\u6570\u503c\uff0c\u524d\u9762\u52a0\u4e0a\u4e00\u4e2a\u628a\u03b1\u770b\u4f5c\u9510\u89d2\u65f6\u539f\u4e09\u89d2\u51fd\u6570\u503c\u7684\u7b26\u53f7\u3002
\u5f53k\u4e3a\u5947\u6570\u65f6\uff0c\u7b49\u4e8e\u03b1\u7684\u5f02\u540d\u4e09\u89d2\u51fd\u6570\u503c\uff0c\u524d\u9762\u52a0\u4e0a\u4e00\u4e2a\u628a\u03b1\u770b\u4f5c\u9510\u89d2\u65f6\u539f\u4e09\u89d2\u51fd\u6570\u503c\u7684\u7b26\u53f7\u3002
\u6269\u5c55\u8d44\u6599
\u4e3e\u4f8b
\u5f530\uff1cx\uff1c\u03c0\uff0f4\u65f6\uff0c\u6c42\u51fd\u6570f\uff08x\uff09\uff1dcosx\uff0fcosxsinx\uff0dsinx\u7684\u6700\u5c0f\u503c\u7684\u65b9\u6cd5\uff1a
f\uff08x\uff09\uff1dcos²x\uff0fcosxsinx\uff0dsin²x
\uff1dcosx\uff0fsinx\uff0dsin²x
\uff1dctgx\uff0dsin²x
ctgx\u57280<x<\u03c0 4\u4e2d\uff0c\u662f\u51cf\u51fd\u6570\uff0c-sin²x\u57280<x<\u03c0 4\u4e2d\uff0c\u4e5f\u662f\u51cf\u51fd\u6570\uff0c\u6240\u4ee5\uff0cf(x)\u57280<x<\u03c0 4\u4e2d\uff0c\u662f\u51cf\u51fd\u6570\u3002
\u5f53x\u6700\u5927\u65f6\uff0cf\uff08x\uff09\u6700\u5c0f\uff0cx\uff1d\u03c0\uff0f4\u65f6\uff0cf\uff08x\uff09\uff1d1\uff0d1\uff0f2\uff1d1\uff0f2
\u6240\u4ee5\uff0cf\uff08x\uff09\u65e0\u9650\u63a5\u8fd11\uff0f
∵2cosx=sin2x/sinx
例: 2cos30°=2X√3/2=√3
sin60°/sin30°=√3/2÷1/2=√3
绛旓細鐭ラ亾cos2x=2cos²x-1鍚?鑰1=sin²x+cos²x,鎵浠2cos²-1=2cos²x-cos²-sin²x=cos²x+sin²x
绛旓細涓夎鍑芥暟浠ｆ崲锛歝os2X=(cosX)^2-(sinX)^2=2*(cosX)^2-1=1-2*(sinX)^2 鍗筹細cos2x=2cosx鐨勫钩鏂-1=cosx鐨勫钩鏂-sinx骞虫柟=1-2sinx鐨勫钩鏂 cos2x鐨勫嚱鏁板浘鍍:
绛旓細浜鍊嶈浣欏鸡鍏紡cos2x=1-2sin^2x鎵浠 cosx=1-2sin^2(x/2)鎵浠 1-cosx = 2sin²(x/2)
绛旓細浜屽嶈浣欏鸡鍏紡鏄鎸囧湪涓夎鍑芥暟涓紝鍙互鐢ㄦ潵璁＄畻2x鐨勪綑寮﹀肩殑鍏紡銆傞氬父锛屾垜浠彲浠ヤ娇鐢ㄤ笅闈㈢殑鍏紡鏉ユ眰瑙ｄ簩鍊嶈浣欏鸡鍊硷細cos 2x = 2cos^2 x - 1 鍏朵腑锛寈鏄鐨勫害鏁帮紝cos鏄綑寮﹀嚱鏁般傚洜姝わ紝濡傛灉鎯宠姹傚嚭cosx鐨勪簩鍊嶈浣欏鸡鍊硷紝鍙互灏唜甯﹀叆涓婇潰鐨勫叕寮忥紝鐒跺悗杩涜璁＄畻銆備緥濡傦紝濡傛灉x = 30掳锛屽垯cos 30掳...
绛旓細涓夎鍑芥暟浠ｆ崲锛歝os2X=(cosX)^2-(sinX)^2=2*(cosX)^2-1=1-2*(sinX)^2 鍗筹細cos2x=2cosx鐨勫钩鏂-1=cosx鐨勫钩鏂-sinx骞虫柟=1-2sinx鐨勫钩鏂 鍊掓暟鍏崇郴锛氣憼 锛涒憽 锛涒憿 鍟嗘暟鍏崇郴锛氣憼 锛涒憽 锛庡钩鏂瑰叧绯伙細鈶 锛涒憽 锛涒憿
绛旓細闄嶅箓鍏紡锛歝os²x=(1+cos2x)/2 sin²x=(1-cos2x)/2 tan²x= sin²x / cos²x=(1-cos2x)/(1+cos2x)鍗囧箓鍏紡锛歴inx=2sin(x/2)cos(x/2)cosx=2cos^2(x/2)-1=1-2sin^2(x/2)=cos^2(x/2)-sin^2(X/2)tanx=2tan(x/2)/ 浜屽嶈鍏紡锛歴in2x...
绛旓細cosx^2鐨勯檷骞鍏紡cos²x=(1+cos2x)/2銆傞檷骞傚叕寮:cosx=(1+cos2x)/2 锛宻inx=(1-cos2x)/2 锛宼anx= sinx / cosx=(1-cos2x)/(1+cos2x)銆浜鍊嶈鍏紡:sin2x=2sinxcosxcos2x=(cosx)^2-(sinx)^2=2(cosx)^2-1=1-2(sinx)^2tan2x=2tanx/[1-(tanx)^2]銆傛敞鎰忥細灏嗕簩鍊嶈鍏紡...
绛旓細cos²x=(cos2x+1)/2 cos²x=cos2x+sin²x cos²x=sin²x/tan²x 浣欏鸡锛堜綑寮﹀嚱鏁帮級锛屼笁瑙掑嚱鏁扮殑涓绉嶃傚湪Rt鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑锛屸垹C=90掳锛堝鍥炬墍绀猴級锛屸垹A鐨勪綑寮︽槸瀹冪殑閭昏竟姣斾笁瑙掑舰鐨勬枩杈癸紝鍗砪osA=b/c锛屼篃鍙啓涓篶osa=AC/AB銆備綑寮﹀嚱鏁帮細f(x)=cos...
绛旓細=[(cosa-sina)^2 + (cosa+sina)^2] / (cosa+sina)(cosa-sina)=2 / [(cosa)^2 - (sina)^2]=2 / (3/5) = 10/3 4.鍘熷紡=sin15掳/cos15掳 + cos15掳/sin15掳 = [(sin15掳)^2 + (cos15掳)^2]/(sin15掳cos15掳)=1/[(1/2)sin30掳] =4 5.鐢遍鎰忥細2cosx-sinx=...
绛旓細cosx鐨勯害鍏嬪姵鏋鍏紡鏄锛歝osx=1-x^2/2i+x^4/4i-x^6/6i+o(x^7)銆傞害鍏嬪姵鏋楀叕寮忔槸娉板嫆鍏紡鐨勪竴绉嶇壒娈婂舰寮忋傜郴鏁颁腑鐢ㄥ埌鐨勪集鍔埄鏁板拰浼姫鍒╁椤瑰紡閮藉彲鐢辫〃鏌ュ緱锛屾晠姝ゅ叕寮忕敤璧锋潵寰堟柟渚裤傛鎷-楹﹀厠鍔虫灄鍏紡鍙互琚湅浣淸a锛宐]涓婃敼鍠勪簡鐨勬褰㈠叕寮忥紝鍙崇绗浜閮ㄥ垎鍙湅鎴愪慨姝ｉ」锛屾渶鍚庨偅椤圭湅鎴愪綑椤广傞害鍏嬪姵...
