1. 1 What you will learn  How to find the value of trigonometric ratios for acute angles of right triangles  More vocabulary than you can possibly stand!

2. Objective: 5-2 Trigonometric Ratios in Right Triangles 2 Visual Vocabulary A B C a b c hypotenuse leg Side opposite A Side adjacent to A

3. Objective: 5-2 Trigonometric Ratios in Right Triangles 3 An Investigation Get the following ratios for both triangles (for 67.4 degree angle). Ratio 1:Ratio 2:Ratio 3: What do you notice? 67.4 o 22.6 o 67.4 o 22.6 o 13 12 5 39 36 15

4. Objective: 5-2 Trigonometric Ratios in Right Triangles 4 More About Ratios These common ratios have names: Sine =Cosine = Tangent = SOHCAHTOA

5. Objective: 5-2 Trigonometric Ratios in Right Triangles 5 Using the Ratios  Example: Find the values of sine, cosine, and tangent for angle B. A B C 18 33

6. Objective: 5-2 Trigonometric Ratios in Right Triangles 6 You Try  Find the values of the sine, cosine, and tangent for angle A. AB C 8 15

7. Objective: 5-2 Trigonometric Ratios in Right Triangles 7 Chart on Page 285  Put it in your notes!

8. Objective: 5-2 Trigonometric Ratios in Right Triangles 8 Other Trigonometric Ratios  There are three other trigonometric ratios.  They are the inverses of sine, cosine, and tangent. They are (chart on page 286): cosecant: secant: cotangent:

9. Objective: 5-2 Trigonometric Ratios in Right Triangles 9 Using Inverse Functions 1. If find sec 2. If, find sin

10. Objective: 5-2 Trigonometric Ratios in Right Triangles 10 Another Example  Find the values of the six trigonometric ratios for angle P. P M N 10 7

11. Objective: 5-2 Trigonometric Ratios in Right Triangles 11 You Try  Find the values of the six trigonometric ratios for angle E. D F E 3 7

12. Objective: 5-2 Trigonometric Ratios in Right Triangles 12 Special Triangles SinCosTanCscSecCot 30 o 45 o 60 o 30 o 60 o 45 o

13. Objective: 5-2 Trigonometric Ratios in Right Triangles 13 One Last Note  On the last slide, did you notice the following: sin 30 o = cos 60 o cos 30 o = sin 60 o Sin and cos are cofunctions. There are other cofunctions: sin = cos[90 o - ] cos = sin[90 o - ] tan = cot[90 o - ] cot = tan[90 o - ] sec = csc[90 o - ] csc = sec[90 o - ]

14. Objective: 5-2 Trigonometric Ratios in Right Triangles 14 Using a Calculator  Sin 72.45 o Cos 53.47 o  Tan 32.763 o  Csc 29.34 o Sec 83.45 o  Cot 27.112 o

15. Objective: 5-2 Trigonometric Ratios in Right Triangles 15 Homework  Page 288, 10-24 even, 28