Question

How do you find the reference angle for `-(3pi)/4`?

Answer 1

the reference angle is `pi/4`

Explanation:

The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.

For `-(3pi)/4`, it will look like this

(Note that if your angle is positive, it will start from 0 and turn anticlockwise, if your angle is negative, it will start from 0 and turn clockwise.)

So, the reference angle is the angle between the terminal side and the x-axis.Lets find out that angle.

And the reference angle is `pi/4`

There is another simpler way to do it.

There is a formula to find the reference angle
`pi*n + theta , n in ZZ` where `theta` is your angle.

So, lets put `n=1` in your case.

`pi*1+(-(3pi)/4) = pi-(3pi)/4 =pi/4`