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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?