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

1 Answer
Jun 27, 2017

the reference angle is #pi/4#


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

enter image source here

(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.

enter image source here

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#