Chapter 12.7, Problem 25E

To determine

To find: the value to the four decimal places by using the first five terms of the trigonometric series; and then compare with the actual value.

Answer to Problem 25E

  $-0.9760$

Explanation of Solution

Given information:

  $\cos \pi$

Calculation:

Use $\cos x\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}$ to evaluate the given value as follows:

  $\begin{array}{c}\cos \pi \approx 1-\frac{{\pi }^2}{2!}+\frac{{\pi }^4}{4!}-\frac{{\pi }^6}{6!}+\frac{{\pi }^8}{8!}\\ \approx -0.9760\end{array}$

Thus, the value is $-0.9760$ .

The actual value of $\cos \pi$ is $-1$ which is approximate to the calculated value.