Estimate f ' (pie/ 4) by using a graphing utility

[priscilla98]

Homework Statement

Let f (x) = sin x. Estimate f ' (pie/ 4) by using a graphing utility.

a) 1 / 4
b) √2 /2
c) 1 / 2
d) pie / 4

The Attempt at a Solution

Is it sin (45) = √2 /2. I'm wondering if b is the answer.

 

[Kevin_Axion]

It is, use the unit circle and it will give you that answer. But it isn't sin(45) it says f'(\frac{\pi}{4}) and f(x)=sinx taking the derivative of f(x) = f'(x)= cosx. Since on the unit circle cos(45)=sin(45) then they both equal \frac{\sqrt{2}}{2}

\frac{d}{dx}sinx = cosx

cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}}