Chapter 10 - NCPN

Practice and Problem Solving
Simplify each expression.
6. 1 – cos 2 θ sin 2 θ 7. tan θ cos θ sin θ
8. sin 2 θ sec θ csc θ tan θ 9. sin 2 θ + tan 2 θ + cos 2 θ sec 2 θ
10. (1 + cot 2 θ)(sec θ) csc 2 θ sec θ 11. sin θ csc θ – cos 2 θ sin 2 θ
12. sec θ cos θ – cos 2 θ sin 2 θ 13. sec θ cos 2 θ csc θ cot θ
Verify each identity. check students’ work; see margin for samples
14. cos θ tan θ = sin θ 15. tan θ (cot θ + tan θ) = sec 2 θ
16. sin θ sec θ = tan θ 17. cos θ + sin θ tan θ = sec θ
18. sec 2 θ = 1 + tan 2 θ 19. sec θ – sin θ tan θ = cos θ
20. cos θ sin θ (cot θ + tan θ) = 1
21. sin 2 θ tan 2 θ = tan 2 θ – sin 2 θ
22. Let sin θ = − 7 and θ be in quadrant III. see margin
25
a. Find cos θ. b. Find tan θ.
23. Let tan θ = − 15 and θ be in quadrant II. see margin
8
a. Find sin θ. b. Find cos θ.
24. How can you express tan θ in terms of cos θ tan θ = ± −
2
1 cos
θ
cosθ
25. How can you express cot θ in terms of csc θ cot θ = ± csc 2 θ −1
26. How can you express sec θ in terms of tan θ sec θ = 2
± 1+
tan θ
27. Mario simplified the
trigonometric expression
sin 2 θ sec 2 θ + 1 as
shown here. What error
did he make Simplify
the expression. see margin
2 2 2
sin θsec θ + 1 = sin θ
1
+ 1
2
sin θ
= 1+
1
= 2
28. Verify the trigonometric identity csc θ tan θ = sec θ.
check students’ work
2 2
29. Simplify the trigonometric expression cot θ − csc θ
2 2
tan θ − sec θ
Mixed Review
Write a recursive formula for each sequence.
30. 7, 2, –3, –8, –13, … 31. 2, –5, 16, –47, 142, …
a n
a n–1
a 1
a n
a n–1
a 1
474 Chapter 10 Trigonometric Functions and Identities
. 1