Question

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

Answer 1

You would look on the unit circle.

Explanation:

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

!unit circle

Answer 2

`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.

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`.