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 Ă˘â€°Ë† x, where x must be in radians.
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Investigate the accuracy of this approximation by creating three plots. For the first, plot sin x and x versus x
for 0 Ă˘â€°Â¤ x Ă˘â€°Â¤ 1. For the second, plot the approximation error sin x Ă˘Ë†â€™ x versus x for 0 Ă˘â€°Â¤ x Ă˘â€°Â¤ 1. For the third, plot
the relative error [sin(x) Ă˘Ë†â€™ x]/sin(x) versus x for 0 Ă˘â€°Â¤ x Ă˘â€°Â¤ 1. How small must x be for the approximation to be
accurate within 5 percent?]