1. Warm up

2. Right Triangle Trigonometry Objective To learn the trigonometric functions and how they apply to a right triangle.

3. The Trigonometric Functions we will be looking at SINE COSINE TANGENT

4. The Trigonometric Functions SINE COSINE TANGENT

5. Prounounced “theta” Greek Letter  Represents an unknown angle

6. opposite hypotenuse adjacent hypotenuse opposite adjacent

7. Finding sin, cos, and tan

8. 6 8 10 SOHCAHTOA

9. Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 9 6 10.8 A

10. Find the values of the three trigonometric functions of . 4 3 ? Pythagorean Theorem: (3)² + (4)² = c² 5 = c 5

11. Sine Find the sin of α 8 10 A C β α

12. Find the sine, the cosine, and the tangent of angle A A 24.5 23.1 8.2 B Give a fraction and decimal answer (round to 4 decimal places).

13. Cosine Find the cosine and tan of α 6 5 √11 A C β α

14. The Reciprocal Trigonometric Ratios Often it is useful to use the reciprocal ratios, depending on the problem. –Cosecant θ is the reciprocal of sine θ, –Secant θ is the reciprocal of cosine θ, and –Cotangent θ is the reciprocal of tangent θ

15. The Reciprocal Trigonometric Ratios

16. Trigonometric Identities

17. Examples 1 Find sec, csc, and cot for angle θ θ

18. Special Angles Special Right Triangles are 30-60-90 and 45-45- 90 √2 1 1 2 1 √3 45 o 30o30o 60 o

19. Fill in the Chart θ in degrees sin θ cos θ tan θ 30 45 60 θ in degrees csc θ sec θ cot θ 30 45 60

20. Relationship between Sine and Cosine sin ( α) = cos ( ) 5 3 4 A C β α

21. Cofunctions Cofunctions of complementary angles are ____________. If θ is an acute angle, then: equal

22. Relationship between Sine and Cosine Look at the Pythagorean Theorem (adj) 2 + (opp) 2 = (hyp) 2 Divide each side by (hyp) 2 (adj) 2 + (opp) 2 = (hyp) 2 (hyp) 2 (hyp) 2 (hyp) 2 (adj) 2 + (opp) 2 = 1 (hyp) 2

23. Relationship between Sine and Cosine (sin (x)) 2 + (cos (x)) 2 = 1 sin 2 (x) + cos 2 (x) = 1

24. Sources lhsblogs.typepad.com/files/section_5.2_rig ht-triangle-trigonometry-2.ppt‎, Oct.1, 2013