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.

Sine: Odd | Cosine: Even

Cosine is sine shifted left by $\frac{π}{2}$.

Amplitude: Vertical distance from midline | Midline: Horizontal center.

Period: Length of one cycle | Frequency: Cycles per unit time.

Concave Up: Curve smiles | Concave Down: Curve frowns.

Period: Time for one cycle | Frequency: Cycles per unit time

Amplitude: Vertical distance from midline | Midline: Horizontal center of the wave

Sine: Starts at midline | Cosine: Starts at maximum/minimum

Vertical: Affects amplitude | Horizontal: Affects period

Positive: Starts increasing | Negative: Starts decreasing

$cos(θ) = sin(θ + \frac{π}{2})$

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

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

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

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

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

$2\pi$

$2\pi$

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

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