Question

What is the exact value of cos(-5pi/4)??

Answer 1

`-(sqrt(2))/2`

Explanation:

You need your Unit Circle for this one. First, convert the negative radian into a positive one by adding `2pi` ( `(8pi)/4` with the common denominator) so you get `(3pi)/4`. Then, find that radian on the Unit Circle and its x-value since you're looking for cosine. Because it's in Quadrant II the x-value is negative and there you have it.

Answer 2

`color(blue)[cos(5pi/4)=-1/sqrt2*(sqrt2/sqrt2)=-sqrt2/2]`

Explanation:

Note that:

`color(red)[cos(-x)=cos(x)]`

`cos(-5pi/4)=cos(5pi/4)`

`5pi/4=225`

`cos(5pi/4)` lies in the third quadrant.

`cosx` is only positive in the first and the forth quadrant.

`cos(5pi/4)=-1/sqrt2*(sqrt2/sqrt2)=-sqrt2/2`