Question

How do you find the linearization at a=pi/4 of `f(x)=cos^2(x)`?

Answer 1

`y=1/2+(pi/4-x)`

Explanation:

A linearization is typically in the form:
`y=f(a)+f'(a) (x-a)` where `a=pi/4`

Finding `f(a)`
`f(pi/4)=cos^2(pi/4)=(sqrt(2)/2)^2=1/2`

Finding `f'(a)`
`f'(a) =-2sin^2(pi/4)=-2(sqrt(2)/2)^2=-1`

Putting it all together:
`y=1/2+(pi/4-x)`