Chapter 9.4, Problem 63E

To determine

To write: The expression in terms of the integer $n$ that represent the $x$ intercept of graph of the given function.

Answer to Problem 63E

The required expression is $a_n=\frac{\pi }{4}+\left(n-1\right)\frac{\pi }{2}$ .

Explanation of Solution

Consider the function.

  $y=\cos 2x$

The graph of the above function is shown below.

  

Figure (1)

The intercept are $\frac{\pi }{4},\frac{3\pi }{4},\frac{5\pi }{4}\mathrm{...}$

The general term for the intercept is given as,

  $a_n=\frac{\pi }{4}+\left(n-1\right)\frac{\pi }{2}$

Therefore, the required expression is $a_n=\frac{\pi }{4}+\left(n-1\right)\frac{\pi }{2}$ .