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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.

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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 ≤ 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?]

 

 
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