1. Aim#10.5: How do we use reference angles to find the exact angle measures?

2. What are Reference Angles?
Reference Angle Relationships:
Let θ be an angle in standard position. The reference angle for θ is the acute angle θ’ formed by the terminal side of θ and the x – axis.

3. Practice:
Find the reference angle and state the quadrant of the terminal side:
EX 1) EX 2) EX 3) EX 4)

4. Evaluating Trigonometric Functions:
Reference angles allow you to evaluate a trigonometric function for any angle θ. The sign of the trigonometric function value depends on the quadrant in which θ lies.
Where are they POSITIVE?
Sin, Csc All
Tan, Cot Cos, Sec
CCW: “Awesome Students Take Challenges”

5. Steps for finding exact values:
1) Draw angle
2) Find reference angle
3) Draw triangle to x – axis
4) Label sides based on reference angle and unit circle
5) Find ratio
6) Check ASTC for sign (diagram above)
Use special triangles and reference angles to find exact values:
EX 5) sin EX 6) sec
EX 7) tan (-2400) EX 8) sec

6. More Practice:
1. Tan –
3. cos
4. sec 1350
sec
2. sin -1500

7. Summary: Answer in complete sentences.
1. What are the three reference angle rules?
2. What are the three important reference angles?
3. What is the cosine and sine of each?
4. How do we find the sec of an angle if we know the cosine?
5. How do we find the tangent of an angle?
6. What are reference angles?