三角函数展开并整理 三角函数题目已经整理好？
\u4e09\u89d2\u51fd\u6570\uff0c\u6c42\u56fe\u4e2d\u6574\u7406\u8fc7\u7a0b\u4e09\u89d2\u51fd\u6570\u5b9a\u4e49
\u628a\u89d2\u5ea6\u03b8\u4f5c\u4e3a\u81ea\u53d8\u91cf\uff0c\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u91cc\u753b\u4e2a\u534a\u5f84\u4e3a1\u7684\u5706\uff08\u5355\u4f4d\u5706\uff09\uff0c\u7136\u540e\u89d2\u7684\u4e00\u8fb9\u4e0eX\u8f74\u91cd\u5408\uff0c\u9876\u70b9\u653e\u5728\u5706\u5fc3\uff0c\u53e6\u4e00\u8fb9\u4f5c\u4e3a\u4e00\u4e2a\u5c04\u7ebf\uff0c\u80af\u5b9a\u4e0e\u5355\u4f4d\u5706\u76f8\u4ea4\u4e8e\u4e00\u70b9\u3002\u8fd9\u70b9\u7684\u5750\u6807\u4e3a(x,y)\u3002
sin(\u03b8)=y;
cos(\u03b8)=x;
tan(\u03b8)=y/x;
\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\u5927\u5168
\u4e24\u89d2\u548c\u516c\u5f0f
sin(A+B) = sinAcosB+cosAsinB
sin(A-B) = sinAcosB-cosAsinB
cos(A+B) = cosAcosB-sinAsinB
cos(A-B) = cosAcosB+sinAsinB
tan(A+B) = (tanA+tanB)/(1-tanAtanB)
tan(A-B) = (tanA-tanB)/(1+tanAtanB)
cot(A+B) = (cotAcotB-1)/(cotB+cotA)
cot(A-B) = (cotAcotB+1)/(cotB-cotA)
\u500d\u89d2\u516c\u5f0f
tan2A = 2tanA/(1-tan² A)
Sin2A=2SinA•CosA
Cos2A = Cos^2 A--Sin² A
=2Cos² A\u20141
=1\u20142sin^2 A
\u4e09\u500d\u89d2\u516c\u5f0f
sin3A = 3sinA-4(sinA)³;
cos3A = 4(cosA)³ -3cosA
tan3a = tan a • tan(\u03c0/3+a)• tan(\u03c0/3-a)
\u534a\u89d2\u516c\u5f0f
sin(A/2) = \u221a{(1--cosA)/2}
cos(A/2) = \u221a{(1+cosA)/2}
tan(A/2) = \u221a{(1--cosA)/(1+cosA)}
cot(A/2) = \u221a{(1+cosA)/(1-cosA)} ?
tan(A/2) = (1--cosA)/sinA=sinA/(1+cosA)
\u548c\u5dee\u5316\u79ef
sin(a)+sin(b) = 2sin[(a+b)/2]cos[(a-b)/2]
sin(a)-sin(b) = 2cos[(a+b)/2]sin[(a-b)/2]
cos(a)+cos(b) = 2cos[(a+b)/2]cos[(a-b)/2]
cos(a)-cos(b) = -2sin[(a+b)/2]sin[(a-b)/2]
tanA+tanB=sin(A+B)/cosAcosB
\u79ef\u5316\u548c\u5dee
sin(a)sin(b) = -1/2*[cos(a+b)-cos(a-b)]
cos(a)cos(b) = 1/2*[cos(a+b)+cos(a-b)]
sin(a)cos(b) = 1/2*[sin(a+b)+sin(a-b)]
cos(a)sin(b) = 1/2*[sin(a+b)-sin(a-b)]
\u8bf1\u5bfc\u516c\u5f0f
sin(-a) = -sin(a)
cos(-a) = cos(a)
sin(\u03c0/2-a) = cos(a)
cos(\u03c0/2-a) = sin(a)
sin(\u03c0/2+a) = cos(a)
cos(\u03c0/2+a) = -sin(a)
sin(\u03c0-a) = sin(a)
cos(\u03c0-a) = -cos(a)
sin(\u03c0+a) = -sin(a)
cos(\u03c0+a) = -cos(a)
tgA=tanA = sinA/cosA
\u4e07\u80fd\u516c\u5f0f
sin(a) = [2tan(a/2)] / {1+[tan(a/2)]²}
cos(a) = {1-[tan(a/2)]^2} / {1+[tan(a/2)]²}
tan(a) = [2tan(a/2)]/{1-[tan(a/2)]^2}
\u5176\u5b83\u516c\u5f0f
a•sin(a)+b•cos(a) = [\u221a(a²+b²)]*sin(a+c) [\u5176\u4e2d\uff0ctan(c)=b/a]
a•sin(a)-b•cos(a) = [\u221a(a²+b²)]*cos(a-c) [\u5176\u4e2d\uff0ctan(c)=a/b]
1+sin(a) = [sin(a/2)+cos(a/2)]²;
1-sin(a) = [sin(a/2)-cos(a/2)]²;
\u5176\u4ed6\u975e\u91cd\u70b9\u4e09\u89d2\u51fd\u6570
csc(a) = 1/sin(a)
sec(a) = 1/cos(a)
\u53cc\u66f2\u51fd\u6570
sinh(a) = [e^a-e^(-a)]/2
cosh(a) = [e^a+e^(-a)]/2
tg h(a) = sin h(a)/cos h(a)
\u516c\u5f0f\u4e00\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u7ec8\u8fb9\u76f8\u540c\u7684\u89d2\u7684\u540c\u4e00\u4e09\u89d2\u51fd\u6570\u7684\u503c\u76f8\u7b49\uff1a
sin\uff082k\u03c0\uff0b\u03b1\uff09= sin\u03b1
cos\uff082k\u03c0\uff0b\u03b1\uff09= cos\u03b1
tan\uff082k\u03c0\uff0b\u03b1\uff09= tan\u03b1
cot\uff082k\u03c0\uff0b\u03b1\uff09= cot\u03b1
\u516c\u5f0f\u4e8c\uff1a
\u8bbe\u03b1\u4e3a\u4efb\u610f\u89d2\uff0c\u03c0+\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0\uff0b\u03b1\uff09= -sin\u03b1
cos\uff08\u03c0\uff0b\u03b1\uff09= -cos\u03b1
tan\uff08\u03c0\uff0b\u03b1\uff09= tan\u03b1
cot\uff08\u03c0\uff0b\u03b1\uff09= cot\u03b1
\u516c\u5f0f\u4e09\uff1a
\u4efb\u610f\u89d2\u03b1\u4e0e -\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08-\u03b1\uff09= -sin\u03b1
cos\uff08-\u03b1\uff09= cos\u03b1
tan\uff08-\u03b1\uff09= -tan\u03b1
cot\uff08-\u03b1\uff09= -cot\u03b1
\u516c\u5f0f\u56db\uff1a
\u5229\u7528\u516c\u5f0f\u4e8c\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u5230\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0-\u03b1\uff09= sin\u03b1
cos\uff08\u03c0-\u03b1\uff09= -cos\u03b1
tan\uff08\u03c0-\u03b1\uff09= -tan\u03b1
cot\uff08\u03c0-\u03b1\uff09= -cot\u03b1
\u516c\u5f0f\u4e94\uff1a
\u5229\u7528\u516c\u5f0f-\u548c\u516c\u5f0f\u4e09\u53ef\u4ee5\u5f97\u52302\u03c0-\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff082\u03c0-\u03b1\uff09= -sin\u03b1
cos\uff082\u03c0-\u03b1\uff09= cos\u03b1
tan\uff082\u03c0-\u03b1\uff09= -tan\u03b1
cot\uff082\u03c0-\u03b1\uff09= -cot\u03b1
\u516c\u5f0f\u516d\uff1a
\u03c0/2\u00b1\u03b1\u53ca3\u03c0/2\u00b1\u03b1\u4e0e\u03b1\u7684\u4e09\u89d2\u51fd\u6570\u503c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a
sin\uff08\u03c0/2+\u03b1\uff09= cos\u03b1
cos\uff08\u03c0/2+\u03b1\uff09= -sin\u03b1
tan\uff08\u03c0/2+\u03b1\uff09= -cot\u03b1
cot\uff08\u03c0/2+\u03b1\uff09= -tan\u03b1
sin\uff08\u03c0/2-\u03b1\uff09= cos\u03b1
cos\uff08\u03c0/2-\u03b1\uff09= sin\u03b1
tan\uff08\u03c0/2-\u03b1\uff09= cot\u03b1
cot\uff08\u03c0/2-\u03b1\uff09= tan\u03b1
sin\uff083\u03c0/2+\u03b1\uff09= -cos\u03b1
cos\uff083\u03c0/2+\u03b1\uff09= sin\u03b1
tan\uff083\u03c0/2+\u03b1\uff09= -cot\u03b1
cot\uff083\u03c0/2+\u03b1\uff09= -tan\u03b1
sin\uff083\u03c0/2-\u03b1\uff09= -cos\u03b1
cos\uff083\u03c0/2-\u03b1\uff09= -sin\u03b1
tan\uff083\u03c0/2-\u03b1\uff09= cot\u03b1
cot\uff083\u03c0/2-\u03b1\uff09= tan\u03b1
(\u4ee5\u4e0ak\u2208Z)
\u8fd9\u4e2a\u7269\u7406\u5e38\u7528\u516c\u5f0f\u6211\u8d39\u4e86\u534a\u5929\u7684\u52b2\u624d\u8f93\u8fdb\u6765,\u5e0c\u671b\u5bf9\u5927\u5bb6\u6709\u7528
A•sin(\u03c9t+\u03b8)+ B•sin(\u03c9t+\u03c6) =
\u221a{(A² +B² +2ABcos(\u03b8-\u03c6)} • sin{ \u03c9t + arcsin[ (A•sin\u03b8+B•sin\u03c6) / \u221a{A² +B²; +2ABcos(\u03b8-\u03c6)} }
\u221a\u8868\u793a\u6839\u53f7,\u5305\u62ec{\u2026\u2026}\u4e2d\u7684\u5185\u5bb9
\u4e09\u89d2\u51fd\u6570\u77e5\u8bc6\u70b9\u6c47\u603b
1.\u7279\u6b8a\u89d2\u7684\u4e09\u89d2\u51fd\u6570\u503c\uff1a
2\uff0e\u89d2\u5ea6\u5236\u4e0e\u5f27\u5ea6\u5236\u7684\u4e92\u5316\uff1a
3.\u5f27\u957f\u53ca\u6247\u5f62\u9762\u79ef\u516c\u5f0f
\u5f27\u957f\u516c\u5f0f\uff1a \u6247\u5f62\u9762\u79ef\u516c\u5f0f:
----\u662f\u5706\u5fc3\u89d2\u4e14\u4e3a\u5f27\u5ea6\u5236\u3002 r-----\u662f\u6247\u5f62\u534a\u5f84
4.\u4efb\u610f\u89d2\u7684\u4e09\u89d2\u51fd\u6570
\u8bbe\u662f\u4e00\u4e2a\u4efb\u610f\u89d2\uff0c\u5b83\u7684\u7ec8\u8fb9\u4e0a\u4e00\u70b9p\uff08x,y\uff09,
(1)\u6b63\u5f26 \u4f59\u5f26 \u6b63\u5207
(2)\u5404\u8c61\u9650\u7684\u7b26\u53f7\uff1a
5.\u540c\u89d2\u4e09\u89d2\u51fd\u6570\u7684\u57fa\u672c\u5173\u7cfb\uff1a
\uff081\uff09\u5e73\u65b9\u5173\u7cfb\uff1a
\uff082\uff09\u5546\u6570\u5173\u7cfb\uff1a
6.\u8bf1\u5bfc\u516c\u5f0f\uff1a\u8bb0\u5fc6\u53e3\u8bc0\uff1a\u628a\u7684\u4e09\u89d2\u51fd\u6570\u5316\u4e3a\u7684\u4e09\u89d2\u51fd\u6570\uff0c\u6982\u62ec\u4e3a\uff1a\u5947\u53d8\u5076\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650\u3002
\u53e3\u8bc0\uff1a\u51fd\u6570\u540d\u79f0\u4e0d\u53d8\uff0c\u7b26\u53f7\u770b\u8c61\u9650\uff0e
8\u3001\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\uff1a
\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570\u5173\u7cfb
\u500d\u89d2\u516c\u5f0f
\u964d\u5e42\u516c\u5f0f\uff1a
\u5347\u5e42\u516c\u5f0f\uff1a
9\uff0e\u89e3\u4e09\u89d2\u5f62
\u6b63\u5f26\u5b9a\u7406 \uff1a
\u4f59\u5f26\u5b9a\u7406\uff1a
\u4e09\u89d2\u5f62\u9762\u79ef\u5b9a\u7406.
15\u3001\u6b63\u5f26\u51fd\u6570\u3001\u4f59\u5f26\u51fd\u6570\u548c\u6b63\u5207\u51fd\u6570\u7684\u56fe\u8c61\u4e0e\u6027\u8d28\uff1a
\u6b63\u786e\uff0c\u5f88\u8be6\u7ec6\u5440
供参考
[cos(-b)-cos a]^2+[sin(-b)-sin a]^2=[cosb-cos a]^2+[sinb+sin a]^2
=(cosb）^2-2cosacosb+(cosa)^2+(sinb)^2+2sinasinb+(sina)^2=2-2cosacosb+2sinasinb=2-2cos(a+b)
两角和公式
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/(1-tanAtanB)
tan(A-B)=(tanA-tanB)/(1+tanAtanB)
cot(A+B)=(cotAcotB-1)/(cotB+cotA)
cot(A-B)=(cotAcotB+1)/(cotB-cotA)
倍角公式
tan2A=2tanA/[1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
sin2A=2sinA*cosA
三倍角公式
sin3a=3sina-4(sina)^3
cos3a=4(cosa)^3-3cosa
tan3a=tana*tan(π/3+a)*tan(π/3-a)
半角公式
sin(A/2)=√((1-cosA)/2) sin(A/2)=-√((1-cosA)/2)
cos(A/2)=√((1+cosA)/2) cos(A/2)=-√((1+cosA)/2)
tan(A/2)=√((1-cosA)/((1+cosA)) tan(A/2)=-√((1-cosA)/((1+cosA))
cot(A/2)=√((1+cosA)/((1-cosA)) cot(A/2)=-√((1+cosA)/((1-cosA))
tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA)
和差化积
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B) )
2cosAcosB=cos(A+B)+cos(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB=2sin((A+B)/2)cos((A-B)/2
cosA+cosB=2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
积化和差公式
sin(a)sin(b)=-1/2*[cos(a+b)-cos(a-b)]
cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]
sin(a)cos(b)=1/2*[sin(a+b)+sin(a-b)]
诱导公式
sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(pi/2-a)=cos(a)
cos(pi/2-a)=sin(a)
sin(pi/2+a)=cos(a)
cos(pi/2+a)=-sin(a)
sin(pi-a)=sin(a)
cos(pi-a)=-cos(a)
sin(pi+a)=-sin(a)
cos(pi+a)=-cos(a)
tgA=tanA=sinA/cosA
万能公式
sin(a)= (2tan(a/2))/(1+tan^2(a/2))
cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2))
tan(a)= (2tan(a/2))/(1-tan^2(a/2))
其它公式
a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [其中,tan(c)=b/a]
a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [其中,tan(c)=a/b]
1+sin(a)=(sin(a/2)+cos(a/2))^2
1-sin(a)=(sin(a/2)-cos(a/2))^2
其他非重点三角函数
csc(a)=1/sin(a)
sec(a)=1/cos(a)
双曲函数
sinh(a)=(e^a-e^(-a))/2
cosh(a)=(e^a+e^(-a))/2
tgh(a)=sinh(a)/cosh(a)
绛旓細tan鐨勬嘲鍕灞曞紑寮忔槸tanx = x+ (1/3)x^3 +...涓嶅悓锛宻inx鏄細sinx = x-(1/6)x^3+...甯哥敤娉板嫆灞曞紑寮廵^x = 1+x+x^2/2!+x^3/3!+鈥︹+x^n/n!+鈥︹︽嘲鍕掑叕寮忔槸灏嗕竴涓湪x=x0澶勫叿鏈塶闃跺鏁扮殑鍑芥暟f(x)鍒╃敤鍏充簬(x-x0)鐨刵娆″椤瑰紡鏉ラ艰繎鍑芥暟鐨勬柟娉曘傝嫢鍑芥暟f(x)鍦ㄥ寘鍚玿0鐨勬煇...
绛旓細鏋勯犱竴涓洿瑙掍笁瑙掑舰蠁灏辨槸鍏朵腑鐨勪竴涓攼瑙掞紝鍐嶅埄鐢涓夎鍑芥暟鐨灞曞紑鍏紡寰楀埌鐨勩備妇渚嬭鏄庯細asinx+bcosx =鈭(a^2+b^2){sinx*锛坅/鈭(a^2+b^2)+cosx*(b/鈭(a^2+b^2)} =鈭(a^2+b^2)sin(x+蠁)cos蠁=a/鈭(a^2+b^2)鎴栬 sin蠁=b/鈭(a^2+b^2)鎴栬 tan蠁=b/a锛埾=arctanb/...
绛旓細娉板嫆灞曞紑寮忓張鍙箓绾ф暟灞曞紑娉 f(x)=f(a)+f'(a)/1!*(x-a)+f''(a)/2!*(x-a)2+...+f(n)(a)/n!*(x-a)n+鈥︹﹀疄鐢ㄥ箓绾ф暟锛歟^x = 1+x+x^2/2!+x^3/3!+鈥︹+x^n/n!+鈥︹n(1+x)=x-x^2/2+x^3/3-鈥︹+(-1)^(k-1)*(x^k)/k(|x|<1)sin x = x...
绛旓細路楂樼瓑浠ｆ暟涓涓夎鍑芥暟鐨勬寚鏁拌〃绀(鐢辨嘲鍕掔骇鏁版槗寰)锛歴inx=[e^(ix)-e^(-ix)]/2 cosx=[e^(ix)+e^(-ix)]/2 tanx=[e^(ix)-e^(-ix)]/[^(ix)+e^(-ix)]娉板嫆灞曞紑鏈夋棤绌风骇鏁帮紝e^z=exp(z)锛1锛媧/1锛侊紜z^2/2锛侊紜z^3/3锛侊紜z^4/4锛侊紜鈥︼紜z^n/n锛侊紜鈥︽鏃朵笁瑙掑嚱鏁板畾涔夊煙宸...
绛旓細涓夎鍑芥暟鍏紡鏈夌Н鍖栧拰宸叕寮忋佸拰宸寲绉叕寮忋佷笁鍊嶈鍏紡銆佹寮︿簩鍊嶈鍏紡銆佷綑寮︿簩鍊嶈鍏紡銆佷綑寮﹀畾鐞嗙瓑銆1绉寲鍜屽樊鍏紡銆俿in伪路cos尾=(1/2)*[sin(伪+尾)+sin(伪-尾)]锛沜os伪路sin尾=(1/2)*[sin(伪+尾)-sin(伪-尾)];cos伪路cos尾=(1/2)*[cos(伪+尾)+cos(伪-尾)];sin伪路...
绛旓細灞曞紑鍏ㄩ儴 涓夎鍑芥暟鍏紡 涓夎鍑芥暟鍏紡鏄暟瀛︿腑鐨勪竴涓噸瑕佹蹇,瀹冧滑鎻忚堪浜嗕笁瑙掑舰鍐呰鍜岃竟鐨勫叧绯汇傞偅涔堜綔涓轰竴鍚嶆暟瀛﹁佸笀鐨勬垜涓哄ぇ瀹鏁寸悊浜嗕笁瑙掑嚱鏁板叕寮忕殑鍑犱釜甯哥敤鍏紡: 姝ｅ鸡瀹氱悊:sinA/a = sinB/b = sinC/c 浣欏鸡瀹氱悊:c² = a² + b² - 2ab cosC 姝ｅ垏瀹氱悊:tanA = a/b 浣欏垏瀹氱悊:cotA = b/a 涓よ鍜...
绛旓細arccosx鐨勬嘲鍕掑叕寮灞曞紑寮忥細Arccosx=蟺/2銆傜煡璇嗘嫇灞曪細arccos琛ㄧず鐨勬槸鍙涓夎鍑芥暟涓殑鍙嶄綑寮︺備竴鑸敤浜庤〃绀哄綋瑙掑害涓洪潪鐗规畩瑙掓椂銆傜敱浜庢槸澶氬煎嚱鏁帮紝寰寰鍙栧畠鐨勫崟鍊硷紝鍊煎煙涓篬0锛屜]锛岃浣測=arccosx锛屾垜浠О瀹冨彨鍋氬弽涓夎鍑芥暟涓殑鍙嶄綑寮﹀嚱鏁扮殑涓诲笺傚弽涓夎鍑芥暟绗﹀彿 arccos琛ㄧず鐨勬槸鍙嶄笁瑙掑嚱鏁颁腑鐨勫弽浣欏鸡銆備竴鑸...
绛旓細娉板嫆灞曞紑寮忓張鍙箓绾ф暟灞曞紑娉 f(x)=f(a)+f'(a)/1!*(x-a)+f''(a)/2!*(x-a)2+...+f(n)(a)/n!*(x-a)n+鈥︹﹀疄鐢ㄥ箓绾ф暟锛歟^x = 1+x+x^2/2!+x^3/3!+鈥︹+x^n/n!+鈥︹n(1+x)=x-x^2/2+x^3/3-鈥︹+(-1)^(k-1)*(x^k)/k(|x|<1)sin x = x...
绛旓細cos伪sin尾 =銆恠in(伪+尾)-sin(伪-尾)銆/2 sin伪sin尾=銆恈os(伪-尾)-cos(伪+尾)銆/2 cos伪cos尾=銆恈os(伪+尾)+cos(伪-尾)銆/2 鍜屽樊鍖栫Н浠ュ強绉寲鍜屽樊鍏紡鐨勬帹瀵奸潪甯哥畝鍗曘俿in(伪+尾)銆乻in(伪-尾)銆乧os(伪+尾)銆乧os(伪-尾)杩欑鏈鍩烘湰鐨涓夎鍑芥暟灞曞紑鍏紡锛屽氨鑳借交鏉炬帉鎻8涓...
绛旓細鍏蜂綋鍥炵瓟濡傚浘锛氬弽姝ｅ鸡鍑芥暟锛堝弽涓夎鍑芥暟涔嬩竴锛変负姝ｅ鸡鍑芥暟y=sinx锛坸鈭圼-½蟺,½蟺]锛夌殑鍙嶅嚱鏁帮紝璁颁綔y=arcsinx鎴杝iny=x锛坸鈭圼-1,1]锛夈傜敱鍘熷嚱鏁扮殑鍥惧儚鍜屽畠鐨勫弽鍑芥暟鐨勫浘鍍忓叧浜庝竴涓夎薄闄愯骞冲垎绾垮绉板彲鐭ユ寮﹀嚱鏁扮殑鍥惧儚鍜屽弽姝ｅ鸡鍑芥暟鐨勫浘鍍忎篃鍏充簬涓涓夎薄闄愯骞冲垎绾垮绉般
