Question

What is the reference angle of -3 radians? Explain.

Answer 1

Reference angle of -3 radians is α= - 171° 53 min 15 sec .

We know the formula for calculating circular arc

Let l=circular arc which ic according to central angle of the circle α

l=((2R π)/360)α  Let l=1 radian and R=1 (unit circle with radius R=1)

1= ((2π)/360)α => α= 360/(2π)= 180/π= 57° 17 min 45sec

Angle of the 1 radian is equal to angle 57° 17min 45sec

According to this

angle of the  -3 radians = -3 ( 57° 17min 45sec) = - 171° 53min 15sec

when you count in the clockwise direction.

Good luck!!!