Precal II ...

Chapter 7 Test

Question 1 Choose the correct right-hand side to make the equation an identity. csc(x)cos(x) = _______

a. 1 b. tan(x) c. cot(x) d. cos2(x)

Question 2 Choose the correct right-hand side to make the equation an identity. sec2(x)sin2(x) = _______

a. 1 b. tan2(x) c. cot2(x) d. sin4(x)

Question 3 Choose the correct right-hand side to make the equation an identity.

sin2 x cosx

+ cosx

1 =?

a. sec(x) b. csc(x) c. 1 d. sin2(x) + 1

Question 4 Convert to a form involving sin x, cos x, and/or tan x using sum or difference

identities. tan( 7 π4 +x) a. tan x – 1 b.

tanx+1 tanx−1

c. tanx−1 tanx+1

d. 1

Question 5 Find the exact value using a sum or difference identity. cos(165°)

a. −1+√2

2 b.

−1−√2 2

c. −√2+√6

4 d.

−√2−√6 4

Question 6 Find the exact value. sin(190°)cos(55°) – cos(190°)sin(55°)

a. 1 2

b. √2 2

c. √3 2

d. −√3 2

Question 7 α and β are quadrant I angles with cos(α) = 15 17

and csc(β) = 41 9

.Find sin(α + β).

a. 185 697

b. 455 697

c. 528 697

d. 672 697

Question 8 α and β are quadrant I angles with cos(α) = 15 17

and csc(β) = 41 9

.Find sin(α - β)

a. 185 697

b. 455 697

c. 528 697

d. 672 697

Question 9 α and β are quadrant I angles with cos(α) = 15 17

and csc(β) = 41 9

. Find tan(α + β).

a. 37 120

b. 91

120 c.

185 672

d. 455 528

Question 10 α and β are quadrant I angles with cos(α) = 15 17

and csc(β) = 41 9

.

Find tan(α - β).

a. 37 120

b. 91

120 c.

185 672

d. 455 528

Question 11 Evaluate exactly as real numbers without the use of a calculator.

cos[sin−1(− 513 )+cos−1(−1213 )] a.

120 169

b. − 119 169

c. 0 d. –1

Question 12 θ=157.5 ° Use a half-angle identity to find the exact value of sin(θ) .

a. √2+√2 2

b. −√2+√2 2

c. √2−√2 2

d. −√2−√2 2

Question 13 sin(x) = 8 17

and π 2

<x<π .Find the exact value of sin(2x).

a. 16 17

b. 120 289

c. − 120 289

d. − 240 289

Question 14 sin(x) = 8 17

and π 2

<x<π .Find the exact value of cos(2x).

a. 7 17

b. 30 17

c. 161 289

d. 220 289

Question 15 sin(x) = 8 17

and π 2

<x<π .Find the exact value of tan(2x).

a. − 240 161

b. − 120 161

c. − 240 289

d. 16 15

Question 16 Find the exact value. tan[2cos−1(−35)] a. −

4 3

b. − 8 3

c. 24 7

d. − 24 7

Question 17 Rewrite the product as a sum involving sine and/or cosine. cos(–4α)cos(–7α)

a. 1 2

cos(3 α)+ 1 2

cos(−11 α) b. 1 2

cos(3 α)− 1 2

cos(−11 α)

c. 1 2

sin(−11α)+ 1 2

sin(3 α) c. 1 2

sin(−11α)− 1 2

sin(3 α)

Question 18 Rewrite the product as a sum involving sine and/or cosine. sin(–10α)sin(–9α)

a. 1 2

cos(−α)+ 1 2

cos(−19 α) b. 1 2

cos(−α)− 1 2

cos(−19 α)

c. 1 2

sin(−19α)+ 1 2

sin(−α) d. 1 2

sin(−19α)− 1 2

sin(−α)

Question 19 Rewrite the product as a sum involving sine and/or cosine. cos(9α)sin(–5α)

a. 1 2

cos(14 α)+ 1 2

cos(4 α) b. 1 2

cos(14 α)− 1 2

cos(4 α)

c. 1 2

sin(4 α)+ 1 2

sin(14 α) d. 1 2

sin(4 α)− 1 2

sin( 14 α)

Question 20 Rewrite the sum as a product involving sine and/or cosine. cos(−7 α)+cos(−3 α)

a. 2cos(–5α)sin(2α) b. 2sin(–5α)cos(2α) c. 2cos(–5α)cos(2α)

d. 2sin(–5α)sin(2α)

Question 21 Find the exact value using an appropriate identity. sin(255°) – sin(–15°)

a. −√ 2 2

b. –1 c. −√3 2

d. −√6 2

Question 22 Solve exactly for 0 ≤ x < 2π. √3tanx−1=0

a. π 6

, 7 π 6

b. π 3

, 4 π 3

c. π 6

, 5 π 6

d. π 3

, 2 π 3

Question 23 Find all real solutions to four decimal places. 3 sin x + 2 = 0

a, x = –0.7297 + 2πk, k any integer b. x = –0.7297 + πk, k any integer

c. x = –0.7297 + πk, x = 3.8713 + πk, k any integer

d. x = –0.7297 + 2πk, x = 3.8713 + 2πk, k any integer

Question 24 Solve for 0° ≤ θ < 360°. √3tan( θ2)+1=0 a. 150° b. 300° c. 150°, 330° d. 300°, 660°

Question 25 The volume of a cone is given by the formula V= 1 3

π r2 hsin (θ) where r is the

radius, h is the slant height of the cone, and θ is the complement of the angle of deflection α.

Find the volume of a cone with radius 2 ft, slant height 12 ft, and angle of deflection α = 26°. Round to four decimal places.

a. 38.3304 ft3 b. 50.2655 ft3 c. 22.0349 ft3 d. 45.1783 ft3