Chapter 6, Problem 36RE

To determine

To find: Amplitude , Period , and Phase shift

Answer to Problem 36RE

Amplitude = $-1$ , Period= $4\pi$ ,Phase shift= $-\pi$

Explanation of Solution

Given information: $y=-\cos \left(\frac{1}{2}x+\frac{\pi }{2}\right)$

Calculation:

For cosine function

  $y=A\cos \left(BX-C\right)+D$

Where , A is amplitude

Period $=\frac{2\pi }{B}$

Phase shift $=\frac{C}{B}$ (from right)

Vertical shift is D

So , by comparing we get

Amplitude = $-1$

Period = $\frac{2\pi }{\frac{1}{2}}=4\pi$

Phase shift = $-\frac{\frac{\pi }{2}}{\frac{1}{2}}=-\pi$

Hence , vertically 0 shift.