1. Precalculus 4.3 Right Triangle Trigonometry 1 Bellwork Rationalize the denominators ·

2. 4.3 Right Triangle Trigonometry Objectives: Evaluate trigonometric functions of acute angles Use the fundamental trigonometric identities Use trigonometric functions to model and solve real-life problems

3. Precalculus 4.3 Right Triangle Trigonometry 3 Trigonometric Functions Given a right triangle with acute angle  opp adj hyp 

4. Precalculus 4.3 Right Triangle Trigonometry 4 Example 1 ·Evaluate the six trig functions of the angle  shown in the right triangle ·sin  = ·cos  = ·tan  = ·csc  = ·sec  = ·cot  = 5 12 13 

5. Precalculus 4.3 Right Triangle Trigonometry 5 Example 2 ·Find the value of x for the right triangle shown x 15 30°

6. Precalculus 4.3 Right Triangle Trigonometry 6 Example 3 ·Solve ∆ABC A B C 62° 6 c b

7. Precalculus 4.3 Right Triangle Trigonometry 7 You Try ·Solve ∆ABC A B C 30° a c

8. Precalculus 4.3 Right Triangle Trigonometry 8 Special Triangles 30º-60°-90° 1 2 30° 60° Recall the conversions 30°=60°=

9. Precalculus 4.3 Right Triangle Trigonometry 9 Special Triangles 45º-45°-90° 1 1 45° Recall the conversion 45°=

10. Precalculus 4.3 Right Triangle Trigonometry 10 Co-functions of Complementary Angles ·Look back at the sines and cosines for the 30-60-90 triangle ·Note that sin 30°=cos 60° ·Co-functions of complementary angles are equivalent

11. Precalculus 4.3 Right Triangle Trigonometry 11 Trigonometric Identities ·Reciprocal Identities

12. Precalculus 4.3 Right Triangle Trigonometry 12 You Try: Classwork ·Label Assignment: CW 4.3 ·Pg. 310: #5, 7, 11

13. Precalculus 4.3 Right Triangle Trigonometry 13 Trigonometric Identities ·Quotient Identities

14. Precalculus 4.3 Right Triangle Trigonometry 14 Trigonometric Identities ·Pythagorean Identities Note: sin 2  is (sin  ) 2 not sin (  2 )

15. Precalculus 4.3 Right Triangle Trigonometry 15 Example 4 ·Given sin  =0.6, find the value of cos  ·Given sin  =0.6, find the value of tan 

16. Precalculus 4.3 Right Triangle Trigonometry 16 Example 5 Use trigonometric identities to transform one side of the equation into the other. ·cos  sec  =1 ·(sec  +tan  )(sec  -tan  )=1

17. Precalculus 4.3 Right Triangle Trigonometry 17 Example 6 ·You are standing 75 meters from the base of the Jin Mao Building in Shanghai, China. You estimate that the angle of elevation to the top of the building is 80°. ·What is the approximate height of the building? ·Suppose one of your friends is at the top of the building. What is the distance between you and your friend?

18. Precalculus 4.3 Right Triangle Trigonometry 18 Closure ·What is the relationship of the sine to the cosecant? ·What is the relationship of the sine to the cosine?

19. Precalculus 4.3 Right Triangle Trigonometry 19 You Try: Classwork ·Label Assignment: CW 4.3 ·Pg. 310: #19, 23, 25-39 odd, 43-63 odd

20. Precalculus 4.3 Right Triangle Trigonometry 20 Homework ·Label Assignment: HW 4.3 ·Pg. 310: #4, 8, 14, 20, 22, 26-38 even, 44-62 even, 70, 74, 76, 78