'''삼각함수,trigonometric_function'''
[[역삼각함수,inverse_trigonometric_function]]
[[쌍곡선함수,hyperbolic_function]]
[[역쌍곡선함수,inverse_hyperbolic_function]]

Sub:
 [[삼각함수의_극한]]
 [[삼각치환,trig_substitution]]

 ||$\sin$ ||$\csc$ ||
 ||$\cos$ ||$\sec$ ||
 ||$\tan$ ||$\cot$ ||

 sine_function  WtEn:sine_function Ggl:"sine function"
 cosine_function WtEn:cosine_function Ggl:"cosine function"
 tangent_function WtEn:tangent_function Ggl:"tangent function"
 cotangent_function WtEn:cotangent_function Ggl:"cotangent function"
 secant_function WtEn:secant_function Ggl:"secant function"
 cosecant_function WtEn:cosecant_function Ggl:"cosecant function"

 or

 [[사인,sine]]
 [[코사인,cosine]]
  [[코사인법칙,cosines_law]]
  [[방향코사인,direction_cosine]]
  [[코사인유사도,cosine_similarity]]
 [[탄젠트,tangent]] ....?

 rel [[sinusoid]] / sinusoidal_function 이었나? spell chk.
  WtEn:sinusoid
  WtEn:sinusoidal_function

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[[TableOfContents]]

= 삼각함수 미분표 =
||(sin x)' = cos x   ||(csc x)' = - csc x cot x ||
||(cos x)' = - sin x  ||(sec x)' = sec x tan x ||
||(tan x)' = sec² x  ||(cot x)' = - csc² x ||

||$\frac{d}{dx}\sin x$||$\cos x$    ||$\frac{d}{dx}\csc x$||$-\csc x \cot x$ ||
||$\frac{d}{dx}\cos x$||$-\sin x$   ||$\frac{d}{dx}\sec x$||$\sec x \tan x $ ||
||$\frac{d}{dx}\tan x$||$\sec^2 x$  ||$\frac{d}{dx}\cot x$||$-\csc^2 x$||

줄이 안맞아서 다른 방식으로.

{{{#!mimetex
$$\huge\begin{array}{|rl|rl|}
\hline
\frac{d}{dx}\sin x &= \cos x    & \frac{d}{dx}\csc x &= -\csc x \cot x\\ \hdash
\frac{d}{dx}\cos x &= -\sin x   & \frac{d}{dx}\sec x &= \sec x \tan x \\ \hdash
\frac{d}{dx}\tan x &= \sec^2 x  & \frac{d}{dx}\cot x &= -\csc^2 x \\
\hline\end{array}$$
}}}

= 삼각함수 미분 증명 =
Moved to [[여러가지증명]]

= 삼각함수 적분 =

= 삼각함수 극한 =
$\lim_{x\to0}\frac{\sin x}x=1$
이것은 보통 squeeze theorem으로 증명. 로피탈로도 가능.
넓이 부등식을...
$\frac12\cos x\sin x<\frac{x}2<\frac12\tan x$
$\cos x<\frac{x}{\sin x}<\frac{1}{\cos x}$
$\cos x<\frac{\sin x}{x}<\frac{1}{\cos x}$
$\lim_{x\to 0}\cos x<\lim_{x\to 0}\frac{\sin x}{x}<\lim_{x\to 0}\frac{1}{\cos x}$

$\lim_{x\to0}\frac{\cos x-1}{x}=0$

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Twin: [[VG:삼각함수,trigonometric_function]]
Up: [[함수,function]]