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 :)