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

2 Answers

You would look on the unit circle.

Explanation:

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

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!unit circle
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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 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#.