Coterminal angles and their trig function values

Question

What is important to remember about coterminal angles and their trigonometric function values?

Answer 1

Coterminal just means two angles end at the same place so they are on the same place in the unit circle. If you have an angle, you can add or subtract 2PI if you are in radians an infinite amount of times and keep getting coterminal angles. If you are in degrees, add or subtract 360. Once you have a coterminal angle (preferably on the unit circle) then you can evaluate the trig function. [We use 360 degrees and 2Pi radians because that is the equivalent of a full circle.]

Ex. Tan (13Pi/4)

13 Pi/ 4 isn't on the unit circle (from 0 to 2Pi), so let's subtract 2Pi (since we are in radians) until we get it on the unit circle.

Get a common denominator for 13Pi/4 and 2Pi which will be a denominator of 4. 2Pi = 8Pi/4

So we have 13Pi/4 -8Pi/4 = 5Pi/4

So 13Pi/4 is coterminal with 5Pi/4 which means the have the same terminal point. You can use your unit circle or your memory to see that 5Pi/4 is in the third quadrant and has a point of (-sqrt of 2 / 2, -sqrt of 2 / 2). Using the coordinate, we can calculate the tangent of the point. Tanx = sinx/cosx. Sinx and cosx are the same for this point, so the tangent is 1.

Tan(13pi/4) = 1

Let me know if you have any questions!