1. Right Triangles
Consider the following right triangle.
Since the triangle is isosceles, the sides opposite the 45° angles are equal in measure. Assign a value of 1 to each side.

2. Use the Pythagorean Theorem to determine the length of the hypotenuse.

3. This 45-45-90 right triangle can give us the trigonometric function values of 45°.

4. This leads us to some important values on the unit circle.
Recall that on the unit circle we have …

5. Consider the point (a,b) on the 45° ray of a unit circle.
Since (a,b) = (cos 45°, sin 45°) , we have

6. In radian form it would be …

7. Moving around the unit circle with reference angles of π/4 we have …

8. Example 1:
Find cos 3π/4
Since cos x is equal to the first coordinate of the point we have …

9. Example 2:
Find sin 5π/4
Since sin x is equal to the second coordinate of the point we have …

10. Example 3:
Find tan (-3π/4)
Since tan x is equal to b/a we have …