Question

If T is the point at a distance 3pi/5 from P(1, 0) on the unit circle with its center at (0, 0), in what quadrant does T lie?

Answer 1

Since 3pi/5 is not one of the normal points we learn on the unit circle let's reason through this.
We know that 180 degrees on the unit circle is pi, or 5pi/5, which is the same as pi.
So 90 degrees is half of 180 and therefore half of 5pi/5 which is 2.5pi/5.

Since 2.5pi/5 is at the 90 degree mark we know that 3pi/5 has to be past this so it will be in Quadrant II.
I hope this helps.