Trigonometric and Polar Functions

$\tan(x) = \tan(-x)$

$\sin(x) = -\sin(-x)$

$\sin(x) = \sin(-x)$

$\cos(x) = -\cos(-x)$

w= $(--(-+))$

w= $+(-(+))$

w= $(-+(-+(+),--(-)))$

w= $+(-(-+))$

x = \pi/6, 5\pi/6

x = \pi/8, 7\pi/8

x = \pi/4, 3\pi/4

x = \pi/3, 2\pi/3

x=-1 and x=3

x=1 and x=3

x=0 and x=2

There is no descent; it continues upwards indefinitely.

$\operatorname{sgn}(-) < -$

$>$

$\neq$

$\geq$

$\theta = 2n\pi$, where $n$ is an integer

$\theta = \frac{(4n+1)\pi}{4}$, where $n$ is an integer

$\theta = \frac{\pi}{2} + 2n\pi$, where $n$ is an integer

$\theta = (2n+1)\pi$, where $n$ is an integer

2

$-\sqrt{3}$

Undefined

$\sqrt{3}$

y = sin(x)

y = sin(2x)

y = sin(x/2)

y = sin(4x)

$\theta = k\pi$ where $k$ is any integer

$\theta = \frac{k \cdot \pi}{1}$ where $k$ is any integer

$\theta = \frac{(k + \frac{1}{2}) \cdot \pi}{1}$ where $k$ is any integer

$\pi = \sqrt{\tan^{\frac{11}{\operatorname{Frac}}}}$ where $k$ is any integer

x = \pi/n - \sqrt{3}/n, where n is a nonzero integer.

x = \pi/6 + n\pi or x = -\pi/6 + n\pi, where n is an integer.

x = \pi/3 + n(2\pi) or x = -\pi/3 + n(2\pi), where n is an integer.

x = (\pi/6 + n\pi)/2 or x = (11\pi/6 + n\pi)/2, where n is an integer.