3.3 Graphs of Circular Functions

What is the amplitude?

Answer explanation

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

What is the period of the graph?

• $2\pi$

• $\pi$

• $4\pi$

• $3\pi$

• $\frac{3\pi}{2}$

Answer explanation

The period is the distance between peaks.

$\frac{5\pi}{2}-\frac{\pi}{2}=\frac{4\pi}{2}=2\pi$

The graph of sine has been transformed in the graph shown. What is the phase shift?

• 3

• 1.429

• -1

• 4.571

• $2\pi$

Answer explanation

y = sin(x) has x-intercept at 0; this graph has x-intercept at 3, so the phase shift was right 3 units.

What is the period?

• $\pi$

• $2\pi$

• $\frac{\pi}{2}$

• $\frac{3\pi}{2}$

• $-1$

Answer explanation

The period is the distance between peaks

What is the amplitude?

• $-3$

• $1$

• $2$

• $4$

• $-2$

Answer explanation

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

The graph of cosine (purple) has been transformed (black).

What is the phase shift?

• $\pi$

• $1$

• $\frac{\pi}{2}$

• $\frac{3\pi}{2}$

• $2\pi$