45-45-90 Right Triangles Consider the following 45-45-90 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.
Use the Pythagorean Theorem to determine the length of the hypotenuse.
This 45-45-90 right triangle can give us the trigonometric function values of 45°.
This leads us to some important values on the unit circle. Recall that on the unit circle we have …
Consider the point (a,b) on the 45° ray of a unit circle. Since (a,b) = (cos 45°, sin 45°) , we have
In radian form it would be …
Moving around the unit circle with reference angles of π/4 we have …
Example 1: Find cos 3π/4 Since cos x is equal to the first coordinate of the point we have …
Example 2: Find sin 5π/4 Since sin x is equal to the second coordinate of the point we have …
Example 3: Find tan (-3π/4) Since tan x is equal to b/a we have …