2. Trigonometric Functions on Right Triangles

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II. I. II.1. A. B. C. 2.3.4. D. E. F. 5. N 70° W6.7. G. H. 8.9.10. I. J.

CONCEPT PREVIEW Determine whether each statement is possibleor impossible. sin θ = 1/2 , csc θ = 2

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II. I. II.1. A. B. C. 2.3.4. D. E. F. 5.6.7. G. H. 8. 270° 9.10. I. J.

CONCEPT PREVIEW Determine whether each statement is possibleor impossible. cos θ = 1.5

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II. I. II.1. A. B. C. 2.3.4. D. E. F. 5.6.7. G. H. 8.9.10. N 70° E I. J.

CONCEPT PREVIEW Determine whether each statement is possibleor impossible. sin² θ + cos² θ = 2

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.(-4, 0)

Use the figure shown to solve Exercises 13–16.Find the bearing from O to A.

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. csc θ , given that sin θ = ―3/7

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.(0, -2)

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.(-3, -3)

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. cot θ , given that tan θ = 18

Concept Check The two methods of expressing bearing can be interpreted using a rectangular coordinate system. Suppose that an observer for a radar station is located at the origin of a coordinate system. Find the bearing of an airplane located at each point. Express the bearing using both methods.(2, 2)

Solve each problem. See Examples 1 and 2.Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.