1. Trigonometry Using Co-terminal and Reference Angles
Dr. Shildneck

2. Co-Terminal Angles
An angle is co-terminal to another angle if their terminal sides end at the same position.
Why are co-terminal angles important?
The trigonometric ratios regarding
co-terminal angles are equivalent.

3. Co-Terminal Angles
600
-3000
420o
-6600

4. Co-Terminal Angles - Degrees
600
600
– 360 = -3000
+ 360= 420o
– 360 – 360 = -6600

5. Co-Terminal Angles - Radians
π/3
π/3
– 2π = -5π/3
+ 2π = 7π/3
– 2π – 2π = -11π/3

6. Reference Angles
The reason that the trigonometry for co-terminal angles are the same is because they have the same reference angles.
Why are reference angles important?
Reference angles allow us to utilize right-triangle trigonometry on the rotational system

7. Reference Angles
A reference angle is the angle that the terminal side makes with the “closest” part of the x-axis.
Reference angles always have a measure between zero and 90 degrees (0 and π/2 radians).
Note: Always form the right angle of a triangle by dropping a perpendicular to the x-axis. (The right angle always touches the x-axis.)

8. Reference Angles (in degrees)
120o
60o
60o
45o
30o
690o
-135o

9. Reference Angles (in radians)
2π/3
π/3
π/3 π
0π, 2π, 4π, …
π/4
π/6
23π/6
5π/4

10. Reference Angles
To determine a reference angle for an angle in standard position, compare the angle’s measure to the closest x-axis. You will either need to subtract using a multiple of 180 (π) or multiple of 360 (2π).
Remember, reference angles always have a measure between zero and 90 degrees (0 and π/2 radians).

11. ASSIGNMENT
Assignment 8