The following small angle approximation for the sine is

Chapter , Problem 1.16

(choose chapter or problem)

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 \(0 \leq x \leq 1\). For the second plot, plot the approximation error sin(x) − x versus x for \(0 \leq x \leq 1\). For the third plot, plot the percent error [sin(x) − x]/sin(x) versus x for \(0 \leq x \leq 1\). How small must x be for the approximation to be accurate within 5%?