Trigonometric and Polar Functions

y = \cos^2(4\theta)

y = -\cos^2(16\theta)

y = -\cos^2(4\theta)

y = \(1/16)\cos^2(2\theta)

$\frac{\sqrt{35}}{6}$

$-\frac{1}{36}$

$\frac{1}{36}$

$-\frac{\sqrt{35}}{6}$

-$\frac{12}{13}$

-$\frac{12}{5}$

$\frac{12}{5}$

$\frac{12}{13}$

-1

0

√2/2

1

θ can take on any values since $\tan(\theta)$'s period ensures it will not repeat values over its domain.

The range of $\tan(\theta)$ must include all real numbers without any restrictions on $\theta$.

The tangent function does not require restrictions because its graph passes the horizontal line test everywhere.

θ must be restricted to an interval where $\tan(\theta)$ is one-to-one, like $(-\pi/2, \pi/2)$.

$\frac{(\text{odd number}) \cdot \pi}{2}$

$(\text{multiple of}) \cdot \frac{\pi}{4}$

$(\text{odd number}) \cdot \pi$

$(\text{even number}) \cdot \pi$

4$\pi$

$\pi$

2$\pi$

$\frac{\pi}{2}$

Hypotenus/Oposite

Opposite/Side

AdjecentSide

Both secant and cosecant functions

Only tangent function

Both sine and cosine functions

Only cotangent function

y = \sin(3x)

y = -\sin(3x)

y = 3\sin(-x)

y = -3\sin(x)