Chapter 12.7, Problem 9CFU

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 9CFU

0.0069

Explanation of Solution

Given information:

  $\sin \pi$

Calculation:

Use $\sin x\approx x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}$ to evaluate the given value as follows:

  $\begin{array}{c}\sin \pi \approx \pi -\frac{{\pi }^3}{3!}+\frac{{\pi }^5}{5!}-\frac{{\pi }^7}{7!}+\frac{{\pi }^9}{9!}\\ \approx 0.0069\end{array}$

Thus, the value is 0.0069.

The actual value of $\sin \pi$ is 0.548 which is approximate to the calculated value.