calculus need help please

Question

4. Find the Linearization of  at . Provide your answer as ?

Answer 1

Use the equation L(x)=f(a)+f'(a)(x-a) where a is pi/2.

1. Find the derivative of f(x) which is sin(x)----> f'(x)=cos(x)
2. Substitute value of a into the parts of the L(x) equation.

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

=sin(a)+cos(a)(x-a)

= sin (pi/2) + cos(pi/2)(x-pi/2)

= 1 + 0 (x-pi/2)

= 1