Once you solve a trigonometric equation for either sin, cos, or tan, then you can see if the positive version of the answer matches the 30, 45, or 60 degree special triangles. If you find a match, then you've found the reference angle. However, if you cannot match it with a special triangle, then you can use either arctan, arccos, or arctan to find the reference angle.
But let's say you were not solving a trig equation. Somebody just gave you a reference angle of 50 degrees (which doesn't match any of the special triangles). You need to know the sides of the reference triangle. The only info that would have for help would be the 50 degrees, as well as the tan, cos, and sin of 50 degrees (which you could find using a calculator or some reference table.).
What would be the next move?
But let's say you were not solving a trig equation. Somebody just gave you a reference angle of 50 degrees (which doesn't match any of the special triangles). You need to know the sides of the reference triangle. The only info that would have for help would be the 50 degrees, as well as the tan, cos, and sin of 50 degrees (which you could find using a calculator or some reference table.).
What would be the next move?