Many applications use the following “small angle” approximation for the sine to obtain a simpler model that is easy to understand and analyze. This approximation states that sin x ≈ x, where x must be in radians. Investigate the accuracy of this approximation by creating three plots. For the first, plot sin x and x versus x for 0 ≤ x ≤ 1. For the second, plot the approximation error sin x – x versus x for 0 ≤ x ≤ 1. For the third, plot the relative error [sin(x) – x]/sin(x) versus x for 0 ≤ x ≤ 1. How small must x be for the approximation to be accurate within 5 percent?
