Trig problem...dividing period into 4 equal parts

Ok so the period is 2pi/3.
It should be 0, pi/6, pi/3, pi/2, 2pi/3
I get you do 2pi/3 times 1/4 to find pi/6 but how do you find the pi/3 and pi/2?

Thanks

You have the right idea.

2pi/3 x 1/4 = 2pi/12 = pi/6, since you're cancelling the 2. You can do some cancelling with the other fractions as well:

2pi/3 x 2/4 = 4pi/12 = pi/3. (cancel 4)

2pi/3 x 3/4 = 6pi/12 = pi/2. (cancel 6)

Why 2/4 and 3/4? Well, if the first period goes from 0 to 1/4 of the whole length, the second will go from 0 to 2/4 (or 1/2) of the length, and the third from 0 to 3/4 of the length.

Make 12 the denominator in all case to get
pi(0, 2/12, 4/12,6/12, 8/12).
Of course, if there is a common factor in num and den you can cancel it. Conversely you can multiply both num and den by the same factor.