Practice and Problem-Solving Exercises

A Practice

Find each value without using a calculator. If the expression is undefined, write undefined. See Problem 1.

9. sec ( − π ) secant open negative pi close
10. csc 5 π 4 co-secant . fraction 5 pi , over 4 end fraction
11. cot ( − π 3 ) co-tangent . open , negative , pi over 3 , close
12. sec π 2 secant , pi over 2
13. cot ( − 3 π 2 ) co-tangent . open . negative , fraction 3 pi , over 2 end fraction . close
14. csc 7 π 6 co-secant . fraction 7 pi , over 6 end fraction
15. sec ( − 3 π 4 ) secant . open . negative , fraction 3 pi , over 4 end fraction . close
16. cot ( − π ) co-tangent open negative pi close

Graphing Calculator Use a calculator to find each value. Round your answers to the nearest thousandth. See Problem 2.

17. sec 2.5
18. csc ( − 0.2 ) co-secant open negative 0.2 close
19. cot 56 ° co-tangent , 56 degrees
20. sec ( − 3 π 2 ) secant . open . negative , fraction 3 pi , over 2 end fraction . close
21. cot ( − 32 ° ) co-tangent open negative 32 degrees close
22. sec 195 ° secant , 195 degrees
23. csc 0
24. cot ( − 0.6 ) co-tangent open negative 0.6 close

Graph each function in the interval from 0 to 2π. See Problem 3.

25. y = sec 2 θ y equals secant 2 theta
26. y = cot θ y equals co-tangent theta
27. y = csc 2 θ − 1 y equals csc 2 theta negative 1
28. y = csc 2 θ y equals csc 2 theta

Graphing Calculator Use the graph of the appropriate reciprocal trigonometric function to find each value. Round to four decimal places. See Problem 4.

29. sec 30 ° secant , 30 degrees
30. sec 80 ° secant , 80 degrees
31. sec 110 ° secant , 110 degrees
32. csc 30 ° co-secant , 30 degrees
33. csc 70 ° co-secant , 70 degrees
34. csc 130 ° co-secant , 130 degrees
35. cot 30 ° co-tangent , 30 degrees
36. cot 60 ° co-tangent , 60 degrees

37. Distance A woman looks out a window of a building. She is 94 feet above the ground. Her line of sight makes an angle of θ with the building. The distance in feet of an object from the woman is modeled by the function d = 94 sec θ . d equals 94 secant theta .  How far away are objects sighted at angles of 25° and 55°? See Problem 5.

B Apply

38. Think About a Plan A communications tower has wires anchoring it to the ground. Each wire is attached to the tower at a height 20 ft above the ground. The length y of the wire is modeled with the function y = 20   csc θ , y equals 20 co-secant theta comma  where θ is the measure of the angle formed by the wire and the ground. Find the length of wire needed to form an angle of 45°.
    • Do you need to graph the function?
    • How can you rewrite the function so you can use a calculator?
39. Multiple Representations Write a cosecant model that has the same graph as y = sec θ . y equals secant theta .

Match each function with its graph.

Table of Contents