1. Right Triangle Trigonometry

2. Degree Mode v. Radian Mode

3. Symbols Theda – Represents the angle measure Hypotenuse Opposite Side Adjacent Side

4. Six Trigonometric Ratios 3 Basic Ratios + 3 Reciprocal Ratios What is a reciprocal?

5. Six Trigonometric Ratios, cont. Basic Trig. Ratio Sine Cosine Tangent Reciprocal Trig. Ratio Cosecant Secant Cotangent It’s a sin to have two c’s.

6. Three Basic Trig. Ratios SOH-CAH-TOA

7. Sine (SOH) 2425 7

8. Cosine (CAH) 2425 7

9. Tangent (TOA) 2425 7

10. Trigonometric Functions, cont. 3 Reciprocal Functions Cosecant – Reciprocal of Sine Secant – Reciprocal of Cosine Cotangent – Reciprocal of Tangent Remember, “It’s a sin to have two C’s”

11. Cosecant – Reciprocal of Sine 2425 7 (“It’s a sin to have two C’s.”)

12. Secant – Reciprocal of Cosine 2425 7

13. Cotangent – Reciprocal of Tangent 2425 7

14. Solving for Side Lengths If given one side and one angle measure, then we can solve for any other side of the triangle. 8 x

15. Solving Right Triangles, cont. 1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? 2. Pick the appropriate trig function to solve for x. 3. Solve for x. 8 x

16. Solving for Side Lengths, cont. 8 x

17. Solving Side Lengths, cont. 7 x

18. Inverse Trigonometric Functions We can “undo” trig ratios Gives us the angle measurement (theta) Represented by a small –1 in the upper right hand corner Ex. 2 nd button → trig ratio

19. Inverse Trigonometric Functions, cont.

20. Experiment: Take the sin –1 (0.75) and the csc (0.75). What do you get? **** sin –1 ≠ csc Ѳ !!!!! ****

21. Your Turn: Solve for theta Round to nearest hundredth

22. Solving For Angle Measures If given two sides of a triangle, then we can solve for any of the angles of the triangle. 54

23. Solving for Angle Measures, cont. 1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse? 2. Pick the appropriate trig function to solve for 3. Solve for using the inverse trigonometric function 54

24. Solving for Angle Measures, cont. 54

25. Your Turn: Complete problems 1 – 6 in the Right Triangle Trigonometry Guided Notes – Part II packet.

26. Answers 1.2.3. 4.5.6.