Question

Use Linear Approximation to estimate
cos(62°) − cos(60°)

Answer 1

L(x)=f'(x)-f'(x)*(x-a)

Answer 2

Put
\[
f[x_]= \cos(x)\\
f'(x)=- \sin(x)\\
f(62) -f(60)= f'(60) 2 =-2 \sin(60) = -\sqrt 3
\]

Answer 3

The derivative of cos(x) is -sin(x) only if x is in radians.
\[
f(x) = \cos(x) \\
f'(x) = -\sin(x) \\
f'(x_1) = -\sin(x_1) \approx \frac{\cos(x_2)-\cos(x_1)}{x_2-x_1}
~~\text{where}~x_1~\text{and}~x_2~\text{are in radians.} \\
\cos(x_2)-\cos(x_1) \approx-\sin(x_1) * (x_2-x_1) \\
\cos(62)-\cos(60) \approx-\sin(60) * (62-60) * \frac{\pi}{180} = -0.03023\\
\]