1. Math III Accelerated Chapter 13 Trigonometric Ratios and Functions 1

2. Warm Up 13.1  In right triangle ABC, a and b are the lengths of the legs and c is the length of the hypotenuse. Find the missing length. Give exact values (radical form, not decimal). 1. a = 6, b = 8 2. c = 10, b = 7 3. If you walk 2.0 km due east and then 1.5 km due north, how far will you be from your starting point? 2

3. 13.1 Use Trigonometry with Right Triangles  Objective:  Use trigonometric functions to find length. 3

4. FunctionAbbreviation Sine sin θ Cosine cos θ Tangent tan θ Cosecant csc θ Secant sec θ Cotangent cot θ Vocabulary 4

5. Right Triangle Definitions of Trigonometric Functions  Let θ be an acute angle.  sin θ =  cos θ =  tan θ = 5 Hypotenuse Adjacent Opposite θ

6. Right Triangle Definitions of Trigonometric Functions  Let θ be an acute angle.  csc θ =  sec θ =  cot θ = 6 Hypotenuse Adjacent Opposite θ

7. Reciprocal Trig Functions  csc θ =  sec θ =  cot θ =  sin θ =  cos θ =  tan θ = 7

8. Example 1  Evaluate the six trig functions of the angle θ. 8 15 8 θ

9. 45˚ – 45˚ – 90˚ Special Triangle 9 45˚ 1 1 θ = 45˚ sin θ =csc θ = cos θ =sec θ = tan θ =cot θ =

10. 30˚ – 60˚ – 90˚ Special Triangle 10 θ = 30˚ sin θ =csc θ = cos θ =sec θ = tan θ =cot θ = 60˚ 30˚ 2 1

11. 30˚ – 60˚ – 90˚ Special Triangle 11 θ = 60˚ sin θ =csc θ = cos θ =sec θ = tan θ =cot θ = 60˚ 30˚ 2 1

12. Example 2  Solve Δ ABC. 12 A B C b c a = 13 56˚

13. Checkpoints 1 & 2 1. Evaluate the six trig functions of the angle θ. 2. Solve Δ ABC. 13 12 θ A B C b 22 a 37˚

14. Angles of Sight  Angle of Elevation The angle made when you look up.  Angle of Depression The angle made when you look down (for ex. from the top of a building). 14 Angle of Elevation Angle of Depression

15. Example 3  You are measuring the height of your school building. You stand 25 feet from the base of the school. The angle of elevation from a point on the ground to the top of the school is 62˚. Estimate the height of the school to the nearest foot. 15

16. Checkpoint 3  A kite makes an angle of 59 ° with the ground. If the string on the kite is 40 feet, how far above the ground is the kite itself? Round to the nearest foot. 16

17. Homework 13.1  Practice 13.1 17