Question

The measure of an angle in standard position is given. find two positive angles and two negative angles that are coterminal with the given angle. (enter your answers as a comma-separated list.) pi/6

Answer 1

Subtracting or adding multiples of 2*r to any angle will make no change, it will be the same angle.
7*pi/6 = 6*pi/6 + pi/6
So, the angle is in the third quadrant and surpasses pi radians by pi/6 radians or 30 degrees.
The positive co-terminal angles are:
Adding 2*pi,
7*pi/6 + 12*pi/6 = 19*pi/6
Adding another 2*pi,
7*pi/6 + 2*(12*pi)/6 = 7*pi/6 + 24*pi/6
7*pi/6 + 24*pi/6 = 31*pi/6
The 2 negative co-terminal angles are:7*pi/6 – 12*pi/6 = 5*pi/6
And
7*pi/6 – 24*pi/6 = -17*pi/6