AP®︎ Precalculus: Topic 3.5 Practice Test

Essential Knowledge: 3.5.A.1

A sinusoidal function is any function that involves additive and multiplicative transformations of $f(\theta)=\sin\theta$. The sine and cosine functions are both sinusoidal functions, with $\cos\theta=\sin\left(\theta+\frac{\pi}{2}\right)$.

Essential Knowledge: 3.5.A.2

The period and frequency of a sinusoidal function are reciprocals. The period of $f(\theta)=\sin\theta$ and $g(\theta)=\cos\theta$ is $2\pi$, and the frequency is $\frac{1}{2\pi}$.

Essential Knowledge: 3.5.A.3

The amplitude of a sinusoidal function is half the difference between its maximum and minimum values. The amplitude of $f(\theta)=\sin\theta$ and $g(\theta)=\cos\theta$ is 1.

Essential Knowledge: 3.5.A.4

The midline of the graph of a sinusoidal function is determined by the average, or arithmetic mean, of the maximum and minimum values of the function. The midline of the graphs of $y=\sin\theta$ and $y=\cos\theta$ is $y=0$.

Essential Knowledge: 3.5.A.5

As input values increase, the graphs of sinusoidal functions oscillate between concave down and concave up.

Essential Knowledge: 3.5.A.6

The graph of $y=\sin\theta$ has rotational symmetry about the origin and is therefore an odd function. The graph of $y=\cos\theta$ has reflective symmetry over the $y$-axis and is therefore an even function.