Chapter 1, Problem 1.16P

The following “small angle” approximation for the sine is used in many engineering applications to obtain a simpler model that is easier to understand and analyze. This approximation states that $\sin x\approx x$ . where x must be in radians. Investigate the accuracy of this approximation by creating three plots. For the first plot, plot sin x and x versus x for $0\le x\le 1$ . For the second plot, plot the approximation error $\sin \left(x\right)-x$ versus x for $0\le x\le 1$ . For the third plot, plot the percent error $\left[\sin \left(x\right)-x\right]/\sin \left(x\right)$ versus x for $0\le x\le 1$ . How small must r be for the approximation to be accurate within 5%?