Question

What is the phase shift of the function y = -cos(3(x+pie/2))-81. Right 3pie/22. Left pie/63. Right pie/2 4. Left pie/2

Answer 1

Answer:

Option D is correct

$left\text{ }\frac{\pi}{2}$

Explanations:

The standard formula for expressing cosine functions is given as:

$y=cos(Bx+C)+D$

The phase shift is given as;

$phase\text{ shift}=-\frac{c}{b}$

Given the function

$\begin{gathered} y=-cos(3(x+\frac{\pi}{2}))-8 \\ y=-cos(3x+\frac{3\pi}{2})-8 \end{gathered}$

Compare with the general function

C = 3pi/2

B = 3

Find the phase shift

$\begin{gathered} Phase\text{ shift}=\frac{-\frac{3\pi}{2}}{3} \\ Phase\text{ shift}=-\frac{3\pi}{6} \\ Phase\text{ shift}=-\frac{\pi}{2} \end{gathered}$

Since the phase shift is negative, hence the shift is to the left.