How do you find the value of cos(pi/4)?

2 Answers
Mar 7, 2018

You would look on the unit circle.

Explanation:

cos(pi/4)= (1/sqrt2) = sqrt2 / 2

enter image source here

!unit circle
enter image source here

Mar 7, 2018

cos(pi/4)=sqrt(2)/2, refer to the explanation below for how to find the exact value without a calculator.

Explanation:

It is possible to find the exact value of cos(pi/4) by constructing a right triangle with one angle set to pi/4 radians.

First, let's convert radians into degrees
pi/4" rad"=pi/4 " rad" * 180^"o"/(pi)* "rad"^-1=45^"o"

Now let's draw a right triangle with one of the acute angles set to 45 degrees. Remeber that these two angles would be supplementary, meaning that their sum would be 90^"o". As a result, the other angle in this triangle would also be 45^"o", making an isosceles right triangle.

An isosceles right triangle with side lengths #1#, #1# and #sqrt(2)#- created with Google Drawings- own workAn isosceles right triangle with side lengths 1, 1 and sqrt(2)- created with Google Drawings- own work

By setting the length of one of the sides adjacent to the right angle to 1 and applying the Pythagorean theorem, you'll find the length of the hypotenuse sqrt(1^2+1^2)=sqrt(2).

Thus cos(pi/4)=cos(45^"o")=("adj.")/("hyp.")=1/sqrt(2)=sqrt(2)/2.