Question

The linear approximation to the function f(x)=cos (9x) at a=pi/2 is L(x)=A+Bx

Answer 1

The derivative at x = pi/2 of f(x) would give you the slope of the linear approximation.
It would give you the B.
To find the A, you know that the line passes through the point (a, f(a))
where a is pi/2 and f(x) is cos 9x.
So the line L passes through (pi/2, cos (9pi/2)).
Given the slope B and a point that the line passes through,
you can solv for the equation of the line L.

Answer 2

but how would you multiply (-sin (9pi/2)) and (x-pi/2)

Answer 3

What is - sin(9pi/2)? That's a number.

Answer 4

i got cos (9pi/2)-x+pi/2