Help me with this "unit circle" problem?

Question

Find the formula for " all angles x such that x is coterminal with 15 degrees"


If you have an answer, did or do you have to use the unti circle for this?
please explain it so i can better understand.

Answer 1

Coterminal means ending in the same place. On your unit circle, 15 degrees is the same as going all the way around (360 degrees) then 15 more so 375 is coterminal with 15. But you could also go twice around + 15 = 720+15 = 735 etc.

So x = 360n + 15 where n = any integer

Answer 2

Yes, the easiest way to do tihs would be by considering the unit circle.
http://www.themathpage.com/aTrig/unit-circle.htm
Think about the angle of 15 degrees sitting on the x axis, and crossing the unit circle.
You could go 360 degrees around the circle and be back where you started, at 375 degrees.
You could go around another 360 degrees for a total of 720 degrees, plus your original 15, and now you're at 735 degrees, but still right back where you started.
So all possible coterminal angles would be 15 + 360n, with n = 0, 1, 2, 3, 4 ...
A related question might be equivalent angles. Again, thinking of the unit circle would help. What other angles between 0 and 360 degrees have 15 degrees as a reference angle?
You could go 15 degrees below the x axis, and you'd be at 345 degrees.
Or you could flip around thru the y axis into the second quadrant, go 15 degrees back from 180, and be at 165 degrees
Or you could go into the third quadrant, go 15 degrees past 180, and be at 195 degrees.
All of these have 15 degrees as their reference angle, and it's fairly easy to do this kind of thing once you are comfortable with the unit circle. So check out the link I've posted, or, if you don't like that one, put trig unit circle in your search window and see if something comes up that you like better.
Trig is a lot easier when you relate it all to the unit circle.

Answer 3

well, coterminal is essentially the same thing as "has 2 rays, the first of which is at 0 (along the X-positive axis), the 2nd is 15 degress around the circle from it"

So, obviously 15 degrees fits, but so does 15+360 (all the way around and back at the 15 degrees), and 15 + 360 + 360, and 15 - 360.

The formula is 15 + (360 * x) for all integer values of x