Download Aim#10.5: How do we use reference angles to find the exact angle

Aim#10.5: How do we use
reference angles to find
the exact angle measures?
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.
Practice:
Find the reference angle and state the quadrant of
the terminal side:
5
7
0
0
EX 1) -130
EX 2) 575
EX 3)
EX 4) 
3
3
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
Tan, Cot
All
Cos, Sec
CCW: “Awesome Students Take Challenges”
Steps for finding exact values:
1) Draw angle
Use special triangles and reference angles to
find exact values:
2) Find reference angle
EX 5) sin 2400
EX 6) sec 17
6
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)
EX 7) tan (-2400)
EX 8) sec
7
4
More Practice:
1. Tan – 3
4
2. sin
3. cos
-1500
7
4
4. sec 1350
5.
sec
11
6
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?