Finding the location of an angle on the unit circle in radians is a lot easier if you imagine counting in multiples of π/2, π/3, π/4 or π/6. For example, to figure out where 5π/3 is on the unit circle, count out “one π/3, two π/3, three π/3 (which is π), four π/3, five π/3.” You’ll get to the right spot every time!
Of course, to make this process work, you do need to know the following relationships
- π/2 = 90°
- π/3 = 60°
- π/4 = 45°
- π/6 = 30°