Find the exact radian measure of the angle.

Question

Find the exact radian measure of the angle. (Simplify your answers completely.)

(a) 140° =?



(b) −10° =?



(c) 235° =?

Answer 1

When it says "exact" and we're looking at radian measure of an angle, that means you will have a pi in your answer.  

 

When it says "simplify", that means you need to kill all the common factors between that angle and 180.

 

So, for the first case, we have 

 

140 degrees * pi/180 radians per degree 

= 140/180 * pi

= 7/8*pi

 

 

Answer 2

Remember the formulas:  degrees = (radianx180)/π

 

                                 radians = (degreesxπ)/180.  This all comes from 2πradians = 360°  so πradians = 180°.