Question

Can someone please show me where I went wrong in the following problem...

Use an appropriate local linear approximation to estimate the value of the given quantity.
cos(31*)

Answer 1

Approximation: cos(pi/6)

x=(pi/6)

f(x)=cos(pi/6)

f'(x)=-sin(pi/6)=-1/2

Answer 2

point: (pi/6,cos(pi/6))

y-cos(pi/6)=-1/2(x-pi/6)

Answer 3

y=-1/2(cos(31pi/180)-pi/6)+cos(pi/6)=.69924

Answer 4

The answer in the book is 0.8573...where did I go wrong?

Answer 5

Well, let's be a little more deliberate about it.

y = cos(x)
sqrt(3)/2 = cos(30º)

dy = -sin(x)*dx
dy = -sin(30º)*(pi/180) = (1/2)*(pi/180)

y + dy = cos(x) - sin(x)dx
y + dy = sqrt(3)/2 - (1/2)*(pi/180) = 0.8573