Which of the following is the best linear approximation for

Question

f(x)=cos(x) near x= π/2 ?

a) y= x - π/2
b) y= -x + π/2
c) y= -x + π/2 + 1
d) y= x - π/2 +1

Answer 1

y(π/2) = 0
y' = -sinx
y'(π/2) = -1
so, using the point-slope form of the line,
y = -1(x-π/2)