Chapter 6.5, Problem 2CFU

To determine

To name: the function for the given situation.

Answer to Problem 2CFU

  $y=\cos \left(x-\frac{\pi }{2}\right)$

Explanation of Solution

Given information:

The graph of function is same as that of $y=\cos x$ with a phase shift of $\frac{\pi }{2}$ .

Calculation:

The equation of cosine function is as follows:

  $y=\cos \left(k\theta +c\right)$

The phase shift is evaluated as follows:

  $\text{Phase shift}=\frac{-c}{k}$

The value of $c$ for the required function will be evaluated as follows:

  $\begin{array}{c}\text{Phase shift}=\frac{-c}{k}\\ \frac{\pi }{2}=\frac{-c}{1}\left[\text{Put the value of }k\text{ and phase shift}\right]\\ c=-\frac{\pi }{2}\end{array}$

Thus the function is same as that of $y=\cos x$ with a phase shift of $\frac{\pi }{2}$ will be $y=\cos \left(x-\frac{\pi }{2}\right)$ .