Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Unit 6 Review

What values for θ (0 ≤ θ < 2π) satisfy the equation?

____ 1. sin 2θ + cos θ = 0

a. π2

, 3π4

, 3π2

, 7π4

c. π2

, 3π4

, 5π4

, 7π4

b. π2

, 7π6

, 3π2

, 11π6

d. 0, π2

, π, 3π2

____ 2. 4 cos2θ sin θ − 3 sin θ = 0

a. π6

, π2

, 5π6

, 7π6

, 3π2

, 11π6

c. 0, π6

, π, 116

b. π2

, π6

, 3π2

, 11π6

d. 0, π6

, 5π6

, π, 7π6

, 11π6

____ 3. Find ALL solutions to: 2 cos 2θ = 1

a. π6

+ 2πk, 5π6

+ 2πb. π3

+ πk, 5π3

+ πk c. π3

, 5π3

d. π6

+ πk, 5π6

+ πk

What is the area of ∆ABC to the nearest tenth of a square meter?

____ 4.

a. 84.5 in.2 b. 93.3 in.2 c. 200 in.2 d. 169.0 in.2

Key

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Name: ________________________ ID: A

2

Use the Law of Sines to find the missing side of the triangle.

____ 5. Find b.

a. 70.1 b. 43.8 c. 57.1 d. 31.5

____ 6. Find the measure of AB given m∠A = 55°, m∠B = 44°, and b = 68.

a. 45.22 c. 88.19b. 96.68 d. 81.12

Use the Law of Sines to find the missing angle of the triangle.

____ 7. Find m∠B to the nearest tenth.

a. 24.6° b. 76.3° c. 65.7° d. 155.4°

B AA 5Law of Sines

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3

Use the Law of Cosines to solve the problem.

____ 8. On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 216 feet deep. The path of the ball makes a 34° angle with the line connecting the pitcher and the catcher, to the right of the pitcher’s mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?

a. 207.4 ft b. 224.3 ft c. 169.3 ft d. 198.7 ft

____ 9. In ∆FGH , g = 8 ft, h = 13 ft, and m∠F = 72°. Find m∠G. Round your answer to the nearest tenth.a. 26.2° b. 35.9° c. 72.1° d. 32.5°

____ 10. Which expression completes the trigonometric identity?

sec π2

− θÊ

Ë

ÁÁÁÁÁˆ

¯

˜̃̃˜̃ =

a. −cos θ b. sin θ c. sec θ d. csc θ

Use a half-angle identity to find the exact value of the trigonometric expression.

____ 11. cos 67.5°

a. −2 + 2

2b.

2 − 22

c. −2 − 2

2d.

2 + 22

____ 12. Given cos θ = 29

and 0° ≤ θ ≤ 90°, find the exact value of sin θ2.

a.223

b.777

c.143

d.77

11

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Solve each triangle. Round your answers to the nearest tenth.

13) In CAB, b = 24.8 m, a = 11.7 m, Cm = 31.9°

14) In QRP, r = 21.4 in, p = 16.2 in, Qm = 97.5°

15) In STR, t = 26 cm, r = 20 cm, Sm = 124°

16) In RPQ, Rm = 48.3°, p = 27 cm, q = 26 cm

17) In BCA, Bm = 24°, a = 25 in, b = 15 in 18) In RST, Rm = 43°, t = 35 cm, r = 32 cm

19) In EFD, Dm = 28°, d = 27 in, f = 7 in 20) In QRP, Qm = 80°, p = 35 in, q = 32 in

Use a double-angle or half-angle identity to find the exact value of each expression.

21) sin 15° 22) sin 120°

23) sin 11212

° 24) sinπ4

LA 22.6013 125.50

C 16 Im

212 48.20P 34.30

9 28 5in

LT 32 5 40.7 cm12 240

217 68.20 r 21.7cmQ 63.50

1LC 113.30 LA 42.70 33.9in 125 88.80 21 48.20 5 46 9cm

2Lc 18.70 LA 137.3 C Il 8in 215 5.20 1 131.80 5 4.3cm

LE 1450 e 33in Not ATriangleLF 70

sin 3 qo

2

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sin 2221 t 252

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Worksheet by Kuta Software LLC-2-

25) sinπ3

26) tan5π8

27) sin θ = 35

and 0 < θ < π2

Find cos 2θ

28) sin θ = −35

and π < θ < 3π2

Find sin 2θ

29) cos θ = −1517

and π2

< θ < π

Find sinθ2

30) cos θ = −45

and 90° < θ < 180°

Find tan 2θ

31) sin θ = 35

and 90° < θ < 180°

Find cos 2θ

32) sin θ = 35

and 0° < θ < 90°

Find tan 2θ

Find the area of each triangle to the nearest tenth. You may need to find some missingdimensions first!

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36) 0 = csc2 θ + 2cot θ 37) 2sin θ + sin θ sec θ = 0

38) −3sin θ − sin θ cos θ = −2sin θ 39) 3 + csc θ = csc2 θ + 1

40) tan2 θ + 1 = 2tan θ 41) sec2 θ + 3 = 7

42) −sec2 θ + 1 = −1 43) cos2 θ + 3 = −2cos θ + 2

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Cumulative Review!

44) Determine if the following functions are even, odd, or neither.

a) f(x) = x3 – 4x

b) f(x) = x5 + 7x2 – 3x + 5

c) f(x) = !"#$% d) f(x) = ""&$! 45) State the end behavior and boundness for the following:

a) f(x) = x3 – 5x

b) f(x) = '"&() "&()

46) Find the extremas and state the intervals of increasing/decresing for the function f(x) = x4 – 2x2 – 8

47). Find the composites for the following:

Ex 3 4LX x3t4x oddCX 5t7C XT 3C X 5 115 7 43

5 Neither

1 46 6 Even

j oddnavetraeeven

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f 2 412 12 I81 2

60

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