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 $$\frac{\sqrt{2}}{2}$$

$$\frac{d}{dx}sinx = cosx$$

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