Question

Find an angle between 0 and 2pi that is coterminal with the following angle. 32pi/9

Answer 1

To do these you will be adding or subtracting  2pi (or integer multiples of .

Since the given angles are in fraction form, it will help to have 2pi  in fraction form, 2pi=10/5=6pi/3=4pi/2=18pi/9     NOTE: this>(/) stands for over like 1 over 2 EX. 1/2

too, so the addition/subtraction is easier.

Hint: When deciding if you have a number between 0 and 2pi, compare it to the fraction version of 2pi that you've been adding/subtracting.


For 17pi/5...
First we can see that 17pi/5 is more than 10pi/5 (aka 2pi). So we need to start subtracting: 17pi/5 - 10pi/5 = 7pi/5

Now we have a number between 0 and 10pi/5. So 7pi/5 is the co-terminal angle between 0 and 2pi.

I'll leave the others for you to do. Just remember that you might have to add or subtract  multiple times before you get a number between 0 and 2pi.
P.S don't add or subtract at all if the number starts out between 0 and 2pi.