$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

$\sec(\theta) = \frac{1}{\cos(\theta)}$

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$x = r \cos(\theta)$

$y = r \sin(\theta)$

$\sin^2(\theta) + \cos^2(\theta) = 1$

$\frac{2\pi}{|B|}$

Amplitude: |A|, Period: $\frac{2\pi}{|B|}$

Find the principal value using $x = \arcsin(a)$, then use the properties of sine to find other solutions within the desired interval.

1. Calculate r: $r = \sqrt{3^2 + 4^2} = 5$. 2. Calculate $\theta$: $\theta = \arctan(\frac{4}{3}) \approx 0.93$ radians.

Set $\cos(2x) = 0$, solve for 2x: $2x = \frac{\pi}{2} + n\pi$, then solve for x: $x = \frac{\pi}{4} + \frac{n\pi}{2}$, where n is an integer.

Create a table of values for $\theta$ and r, plot the points (r, $\theta$), and connect them to form the graph (usually a circle).

Use trigonometric identities to simplify the equation, then solve for the multiple angle, and finally solve for the variable.

Identify the midline of the function. The vertical shift is the distance between the midline and the x-axis.

For $y = A\tan(Bx + C) + D$, the period is $\frac{\pi}{|B|}$.

Consider the range of the original trigonometric function. For example, the domain of $\arcsin(x)$ is [-1, 1].

Replace x with $r\cos(\theta)$ and y with $r\sin(\theta)$, then simplify the equation.

Patterns that repeat over time.

Periodic functions represented by sine or cosine.

Functions that find angles from given sine, cosine, or tangent values.

Another way to express positions in a plane using distance and angle.

The maximum displacement from the midline of the function.

The length of one complete cycle of the function.

A transformation that moves the graph of a function up or down.

A circle with radius 1 centered at the origin, used to define trigonometric functions.

A unit of angular measure defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

A function defined in polar coordinates, typically in the form r = f(θ).