How do you change #(-3pi)/2# radians to degree measure?

1 Answer
May 16, 2015

To convert a radian measure to degrees, multiply by #{180 \quad ^o}/{pi \quad \text{radians}}#

#{-3pi}/2 \text{radians}={-3pi}/2 \text{radians} *{180 \quad ^o}/{pi \quad \text{radians}} = -270\quad^o#

,

In the multiplication, the unit of radians cancels out which leaves the result in terms of degrees.

There are #180# degrees in #pi# radians. Therefore, multiplying by

#{180 \quad ^o}/{pi \quad \text{radians}}# is the same as multiplying by #1# which doesn't change

the actual size of the angle.