Question

1. what is the amplitude of this sinusoidal function?

image of a sinusoidal graph
a. 3
b. 2π
c. 6
d. -3

1. what is the period of the function y = tan 5x?

a. -π/5
b. 5/π
c. 2π/5
d. π/5

Explanation:

Question 20

Step1: Recall amplitude definition

Amplitude of a sinusoidal function \( y = A\sin(Bx - C)+D \) (or cosine) is \( |A| \), the distance from midline to peak (or trough).

Step2: Identify midline and peak

From the graph, midline (average of max and min) is \( y = 0 \) (since max is \( 3 \), min is \( -3 \), midline \( \frac{3 + (-3)}{2}=0 \)). Peak value is \( 3 \), so amplitude is \( |3 - 0| = 3 \). Negative amplitude doesn’t make sense (amplitude is magnitude), so ignore \( -3 \).

Step1: Recall tangent period formula

The period of \( y = \tan(kx) \) is \( \frac{\pi}{|k|} \).

Step2: Apply formula to \( y = \tan(5x) \)

Here, \( k = 5 \), so period \( = \frac{\pi}{|5|}=\frac{\pi}{5} \).

Answer:

A. 3

Question 21