Question

The measure of angle θ is 7 pi/6 . The measure of its reference angle is... °?, and sin θ is ...?

Answer 1

Alright, let get started.

We have given the angle Ф as 7π/6.

And we are asked to find its reference angle (in dgrees)

So, we will first change 7π/6 from radian to degrees by multiplying 180/π

Ф = 7π/6 * 180/π

Ф = 7 * 180/6 = 210 degrees

Now, reference angle is the angle between X axis and the terminal side of given angle.

Please refer to the diagram attached.

The terminal side of angle 210 is lying in 3rd quadrant.

The angle between X axis and its terminal side is 210 - 180 = 30 degrees

Hence refernce agle of 210 degree or 7π/6 is 30 degrees. : Answer

We are also asked to find sin Ф

We could find it by using unit circle. sin 210 = - 1/2 Answer

Hope it will help :)