\(0^o\)
\(30^o\)
\(45^o\)
\(60^o\)
\(90^o\)
sin
0
\(\frac{1}{2}\)
\(\frac{1}{2}\sqrt{2}\)
\(\frac{1}{2}\sqrt{3}\)
1
cos
1
\(\frac{1}{2}\sqrt{3}\)
\(\frac{1}{2}\sqrt{2}\)
\(\frac{1}{2}\)
0
tan
0
\(\frac{1}{3}\sqrt{3}\)
1
\(\sqrt{3}\)
\(\infty\)
\(\int \sec ^2 x dx = \tan x + c\\
\int cosec ^2 x dx = \cot x + c\\
\int \sec x \tan x dx = \sec x + c\\
\int cosec \cot x dx = -cosec x + c\\
\int \tan x dx = ln|\sec x| + c\\
\int \cot x dx = -ln |cosec x| + c\\
\int \sec x dx = ln |\sec x tan x| + c\\
\int cosec x dx = -ln |cosec x + cot x| + c\\
\)
\(f(x)=\tan x \quad maka \quad f’(x)=\sec ^2 x\\
f(x)=\cot x \quad maka \quad f’(x)= -cosec ^2 x\\
f(x)=\sec x \quad maka \quad f’(x)=\sec x \tan x\\
f(x)=cosec x \quad maka \quad f’(x)= -cosec x \cot x\\
\)
\(\lim{x\to0}\frac{\sin ax}{ax}=\lim{x\to0}\frac{\tan ax}{ax}=\lim{x\to0}\frac{ax}{\sin ax}= \lim{x\to0}\frac{ax}{\tan ax}=1\\ \lim{x\to0}\frac{\sin ax}{bx}=\lim{x\to0}\frac{\tan ax}{bx}=\lim{x\to0}\frac{ax}{\sin bx}= \lim{x\to0}\frac{ax}{\tan bx}=\frac{a}{b} \)
\(Jika \quad \cos x= \cos A \quad maka\\
x_{1,2} = \pm A + k.360^o\\
Jika \quad \tan x= \tan A \quad maka\\
x = A + 180^o\\\)
Catatan,
Jika terdapat persamaan cos x = sin A, cot x = tan A, sec x = cosec A atau sebaliknya, maka salah satu diubah menjadi (90 – A)o
Misalnya, cos x = sin A menjadi cos x = cos (90 – A)o