SOLUTION: Find an angle, in radian measure, between 0 and 2pi that is coterminal with the given angles. a) 17pi/5 b) -13pi/3 c) 53pi/2 d) 17pi/9

Algebra ->  Trigonometry-basics -> SOLUTION: Find an angle, in radian measure, between 0 and 2pi that is coterminal with the given angles. a) 17pi/5 b) -13pi/3 c) 53pi/2 d) 17pi/9       Log On


   

Question 826174: Find an angle, in radian measure, between 0 and 2pi that is coterminal with the given angles.
a) 17pi/5
b) -13pi/3
c) 53pi/2
d) 17pi/9

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
To do these you will be adding or subtracting 2pi (or integer multiples of 2pi%7D%7D%29+until+you+get+a+number+between+0+and+%7B%7B%7B2pi.

Since the given angles are in fraction form, it will help to have 2pi in fraction form, too, so the addition/subtraction is easier.
2pi+=+10pi%2F5+=+6pi%2F3+=+4pi%2F2+=+18pi%2F9
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%2F5...
First we can see that 17pi%2F5 is more than 10pi%2F5 (aka 2pi). So we need to start subtracting:
17pi%2F5-10pi%2F5=7pi%2F5
Now we have a number between 0 and 10pi%2F5. So 7pi%2F5 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 2pi 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!