Linear approximation of cos(28 degrees)

$\begingroup$

Evaluate cos(28 degrees) using linear approximation.

I have done this so far, but the answer seems to be incorrect and I can't figure out why.

y= 30
f(x) = cos(x)
f'(x) = -sin(x)
f(y) = f(30) = cos(30) = sqrt(3)/2
f(y) = f(30) = -sin(30) = -1/2
f(x) = f(y) + f(y) (x-y) = sqrt(3)/2 + -1/2 (28-30) = sqrt(3)/2 + 1 = 1.866025404

$\endgroup$ 4

1 Answer

$\begingroup$

You are forgetting to account for unit conversion. What you have is $f(x) = \cos( \pi/180 \cdot x )$, so $f'(x) = -\sin(\pi/180 \cdot x ) \cdot \pi/180$. Then you will get

$$ f(28) \approx f(30) + f'(30) \cdot (28-30) = \cos( \pi/6 ) - \sin(\pi/6) \cdot \pi/180 \cdot -2 = 0.883478\dots $$

$\endgroup$ 7

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy