Reference Angles

1. Reference Angle (α)

• Any angle around a circle can be turned into a right triangle using a reference angle (α).

• Using this we can calculate any angle around the center of a circle.

• Depending on the Quadrant (I, II, III, IV) the initial side of the refence angle changes.

​How to find the angle using a reference angle by quadrant:

2. Finding Trig Ratios using reference angles and a unit circle.

• Unit Circle- all the angles around the origin of a circle that can be used to form a right triangle.

• We can use the unit circle and special right triangles to find the values of common angles trig ratios.

​Special Right Triangles you should know:

​1

​1

​1

​-1

​1

​-1

​1

​-1

All Students Take Calculus

​All are +.

​Sine is +.

Tangent is +.

Cosine is +.

3. Using the Unit Circle.

The Unit Circle is used to find the sine, cosine and tangent values for all the angles around the circle with a reference angle of 30°, 45°, 60° and 90°.

Ex. Find the sine, cosine and tangent of 300°.