Linear Approximations

Question

How do I use linear approximations to find cos(π/3 + 3/100) using a=π/3 ?

Answer 1

The tangent line equation is y = f'(a)*(x-a) + f(a), so y = -sin(pi/3)*(x-pi/3) + cos(pi/3) = (sqrt(3)/2)*(x-pi/3) + 0.5

So now plug in 3/100: y = -(sqrt(3)/2)*( (pi/3 + 3/100) - (pi/3) ) + 0.5 = -(sqrt(3)/2)*( 3/100 ) + 0.5

= about 0.474