Measure the distance for one complete cycle.

Average of the maximum and minimum y-values.

Half the difference between max and min y-values.

A vertical translation of the function.

It stretches or compresses the graph horizontally.

It stretches or compresses the graph vertically.

Curve looks like a smile.

Curve looks like a frown.

The derivative, $cos(x)$, represents the slope of $sin(x)$ at each point.

The derivative, $-sin(x)$, represents the slope of $cos(x)$ at each point.

A function resembling sine or cosine, oscillating and periodic.

The length of one complete cycle.

Number of cycles per unit time; reciprocal of period.

The horizontal line that cuts the wave in half.

Vertical distance from midline to max/min value.

Symmetry about the origin; f(-x) = -f(x).

Symmetry about the y-axis; f(-x) = f(x).

Up and down movement between two values, creating a wave.

The curve looks like a smile.

The curve looks like a frown.

$cos(θ) = sin(θ + \frac{π}{2})$

$f = \frac{1}{T}$

$k = \frac{y_{max} + y_{min}}{2}$

$Amplitude = \frac{y_{max} - y_{min}}{2}$

$f(-x) = -f(x)$

$f(-x) = f(x)$

$2\pi$

$2\pi$

$\frac{1}{2\pi}$

$\frac{1}{2\pi}$