Question: MATLAB QUESTION Many engineering applications use the small angle approximation for the sine function to obtain a simpler model that is easier to analyze. This

MATLAB QUESTION

Many engineering applications use the "small angle" approximation for the sine function to obtain a simpler model that is easier to analyze. This approximation states that sin(x) = x, where x is in radians. Investigate the accuracy of this approximation by plotting sin(x) vs. x and fitting a line through it.

(a) How small must x be so that the error [sin(x)-x]/sin(x) is less than 5%? Less than 1%?

(b) Make a plot of x vs. sin(x) for values from 0 to pi/2. Calculate the equation for the best-fit line (you can use "Basic Fitting" for this). Do this for different maximum values of x. What range of x values would you consider to give you an acceptable fit? (Hint: What should the coefficients of your best-fit line be for a perfect fit?)

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