1. Trigonometric Ratios in the Unit Circle 6 December 2010

2. Trigonometric Ratios in the Unit Circle The unit circle has a radius of 1

3. Trigonometric Ratios in the Unit Circle, cont. The tangent and cotangent formulas stay the same

4. “All Students Take Calculus” AS CT all functions are positive sine is positive tangent is positive cosine is positive

5. Example: Trigonometric Function Sine Cosine Tangent Cosecant Secant Cotangent

6. Example: –240° Trigonometric Function Sine Cosine Tangent Cosecant Secant Cotangent

7. Special Right Triangles 30° 60° 45° 30-60-9045-45-90

8. Special Right Triangles & the Unit Circle

11. Evaluating Trigonometric Expressions Step 1: Substitute the correct exact value for the trigonometric function Step 2: Evaluate using the order of operations

12. Evaluating Trigonometric Expressions, cont.

13. Reference Angles Reference angles make it easier to find exact values of trig functions in the unit circle Always Acute (less than 90°) Have one side on the x-axis

14. Finding Reference Angles Step 1: Sketch a graph of theda Step 2: Find the acute angle that is coterminal with theda and has one side on the x-axis

15. Finding Reference Angles Step 3: Solve the trig functions for the reference angle Step 4: Adjust the signs of your solution depending on the quadrant