Free Printable Precalc Test 10

1.

Trig Functions tell us what?

a)

sides

b)

angles

c)

Relationship between the ratio of side lengths at a given angle

d)

nothing

2.

Since $g\left(x\right)=\sin\left(x\right)$ is not one to one, it does not have an inverse.

a)

True

b)

False

3.

What test will you use to determine if a function is one-to-one?

a)

Veetical Line Test

b)

Horizontal Line Test

c)

One-to-one Test

d)

Function Domain-Range Test

4.

True or False: $\arcsin\left(x\right)$ is another way to write $\sin^{-1}\left(x\right)$ .

a)

TRUE!

b)

FALSE!

5.

Domain of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

6.

In which two quadrants is inverse sine defined?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

7.

Which can be a restriction for the domain of y = cos x so the inverse cosine can be a function?

a)

$\left[-\frac{\pi}{2},\ \frac{\pi}{2}\right]$

b)

$\left[0,\ \pi\right]$

c)

$\left(-\frac{\pi}{2},\ \frac{\pi}{2}\right)$

d)

$\left[0,\ 2\pi\right]$

8.

Range of function $\cos^{-1}x\ is$

a)

$\left[0,\ \pi\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

9.

In which two quadrants is inverse cosine defined?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

10.

Range of function $\tan^{-1}x\ is$

a)

R

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$R-\left\{\frac{\pi}{2}\right\}$

d)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

11.

Choose the correct ratio.

a)

sin^-1(9/20)

b)

tan^-1(9/20)

c)

cos^-1(9/20)

d)

cos^-1(20/9)

12.

Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$-\frac{\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$-\frac{\pi}{6}$

d)

$\frac{\pi}{6}$

13.

The value of $\sin^{-1}\left(-\frac{1}{2}\right)\$

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

$-\frac{\pi}{3}$

d)

$-\frac{\pi}{6}$

14.

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

a)

$\frac{5\pi}{6}$

b)

$-\frac{5\pi}{6}$

c)

$\frac{\pi}{6}$

d)

$-\frac{\pi}{6}$

15.

Find the exact value of $\tan^{-1}\left(\frac{\sqrt{3}}{3}\right)$ .

a)

$\frac{\pi}{6}$

b)

$\frac{3\pi}{4}$

c)

$\frac{2\pi}{3}$

d)

$\frac{5\pi}{6}$

16.

Find the exact value of $\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ .

a)

$\frac{\pi}{6}$

b)

$-\frac{\pi}{4}$

c)

$\frac{\pi}{4}$

d)

$\frac{\pi}{3}$

17.

Determine the measurement of the missing angle.

Hint: Use inverse trig functions + input ratio in calculator

a)

90º

b)

37°

c)

36°

d)

10º

18.

Find the values of the six trigonometric functions for θ.

HINT - SOH CAH TOA - Set up ratios and simplify the fraction.

a)

$\frac{24}{25}$

1.

sin x

b)

$\frac{7}{25}$

2.

cos x

c)

$\frac{7}{24}$

3.

tan x

d)

$\frac{25}{7}$

4.

sec x

e)

$\frac{25}{24}$

5.

csc x

19.

What is the period of $y=4\cos\left(2x\right)$ ?

Hint*** For sin/cos: $Period\ =\frac{2\pi}{B}$

a)

4π

b)

π

c)

2π

d)

π/2

20.

Write the equation for a sine function with an amplitude of 6 and a period of $\frac{\pi}{4}$ .

a)

$y=6\sin8\theta$

b)

$y=6\sin8\left(\theta-1\right)$

c)

$y=6\sin\ \frac{1}{4}\theta$

d)

$y=6\sin\theta$

21.

What is the period of $y=4\tan5x$ ?

Hint*** For tangent: $Period\ =\frac{\pi}{B}$

a)

π/5

b)

π

c)

5

d)

5π

e)

2π/5

22.

Write the "Sine" equation given:

Period: $8\pi$

Amplitude: 3

Phase Shift: None

Vertical Shift: up 1

Remember: Asin(Bx-C) + D

a)

$y=3\sin\left(4x\right)+1$

b)

$y=\sin\left(\frac{1}{4}x\right)+3$

c)

$y=3\sin\left(\frac{1}{4}x\right)+1$

d)

$y=\sin\left(4x\ -1\right)+3$

e)

none of these

23.

a)

-π/3

b)

4π/3

c)

-2π/3

d)

2π/3

24.

a)

0

b)

π/2

c)

2π

d)

3π

25.

a)

3π/4

b)

π/4

c)

5π/4

d)

-3π/4

26.

a)

π/6

b)

5π/6

c)

7π/6

d)

2π

27.

a)

π/2

b)

π

c)

3π/2

d)

-3π/2

28.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

29.

arccos (-√3/2)

a)

5π/6

b)

2π/3

c)

-π/6

d)

7π/6

30.

What is tan[arccos(-1)]?

a)

undefined

b)

0

c)

½

d)

1

31.

Evaluate the function: tan[sin^-1(-1/2)]

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

32.

cos^-1[tan(-π/4)] =

a)

0

b)

π

c)

π/4

d)

3π/4

33.

Find all solutions for $X$ between the interval $0\le X<2\pi:$

$\cos2X=-\frac{\sqrt[]{3}}{2}$

a)

$\frac{5\pi}{12},\ \frac{7\pi}{12},\ \frac{17\pi}{12},\ \frac{19\pi}{12}$

b)

$\frac{5\pi}{12},\ \frac{7\pi}{12},\ \frac{11\pi}{12},\ \frac{19\pi}{12}$

c)

$\frac{\pi}{12},\ \frac{5\pi}{12},\ \frac{17\pi}{12},\ \frac{19\pi}{12}$

d)

$\frac{\pi}{3},\ \frac{3\pi}{2},\ \frac{5\pi}{3},\ \frac{7\pi}{6}$

34.

Find all solutions for $X$ between the interval $0\le X<2\pi:$

$\sin2x=\frac{1}{2}$

a)

$\frac{\pi}{12},\ \frac{5\pi}{12},\ \frac{13\pi}{12},\ \frac{19\pi}{12}$

b)

$\frac{\pi}{12},\ \frac{5\pi}{12},\ \frac{13\pi}{12},\ \frac{17\pi}{12}$

c)

$\frac{\pi}{12},\ \frac{5\pi}{12},\ \frac{7\pi}{12},\ \frac{17\pi}{12}$

d)

$\frac{\pi}{3},\ \frac{4\pi}{3},\ \frac{5\pi}{3},\ \frac{8\pi}{3}$

35.

Find all solutions for $X$ between the interval $0\le X<2\pi:$

$\tan2x=0$

a)

$0,\ \frac{\pi}{2},\ \frac{3\pi}{2},\ 2\pi$

b)

$0,\ \pi,\ \frac{3\pi}{2},\ \frac{11\pi}{6}$

c)

$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2}$

d)

$0,\ \frac{\pi}{2},\ \pi,\ 2\pi$

36.

Find all solutions for $X$ between the interval $0\le X<2\pi:$

$\sin3x=1$

a)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \pi$

b)

$\frac{\pi}{3},\ \frac{5\pi}{3},\ \frac{3\pi}{2}$

c)

$\frac{\pi}{6},\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

d)

$\frac{\pi}{6},\ \frac{5\pi}{6},\ \frac{3\pi}{2}$

37.

Why doesn't 2cosx − 3 = 0 have solutions?

a)

cos x is never bigger than one

b)

cos x is never equal to a fraction

c)

Actually, this equation does have a solution, x = π

d)

This equation will have a solution tomorrow.

38.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

39.

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

a)

divide tanx from both sides

b)

factor out tanx

c)

subtract 2 tanx from the left and then factor tanx out

d)

cancel sin²x out

40.

Factor 0 = sin²x − sinx

a)

0 = sinx(sinx)

b)

0 = sinx(1 − sinx)

c)

0 = cosx(sinx − 1)

d)

0 = sinx(sinx − 1)

41.

csc²x = 2 is equivalent to sin²x = ½

a)

True

b)

False

42.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

43.

Solve for all values of x over the interval [0,2π]

a)

$\frac{3π}{4}and\ \frac{5π}{4}\$

b)

$\frac{π}{4}and\ \frac{3π}{4}$

c)

$\frac{π}{4},\frac{3π}{4},\frac{5π}{4}\ and\ \frac{7π}{4}$

d)

$\frac{\pi}{6}\ and\ \frac{5\pi}{6}$

44.

Solve equation for $0\le\theta<2\pi$ .
$2+3\csc\theta+2\csc^2\theta=\csc^2\theta$

a)

$\theta=\frac{3\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{7\pi}{6},\frac{3\pi}{2},\frac{11\pi}{6}$

d)

$\theta=\frac{\pi}{4},\frac{11\pi}{6}$

45.

Solve equation for $0\le\theta<2\pi$ .
$-1-2\sec^2\theta=-3\sec^2\theta$

a)

$\theta=0,\pi,\frac{4\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

d)

$\theta=0,\pi$

46.

Solve each equation using a calculator. Round to the nearest hundredth.

$4+3\cos x=3.06+2\cos x$

a)

$35.90\degree,\ 160.05\degree\$

b)

$199.95\degree$

c)

$160.05\degree,\ 199.95\degree$

d)

No solution.

47.

Solve each equation using a calculator. Round to the nearest hundredth. $5+4\cot\theta=12.72$

a)

$264.86\degree$

b)

$27.39\degree,\ 207.39\degree$

c)

$27.39\degree,\ 264.86\degree$

d)

No solution.

48.

Solve on the Interval [0,2π)
tan(x) + 1 = 0

a)

x = π/4, x = 5π/4

b)

x = π/4, x = 3π/4

c)

x = π/2

d)

x = 3π/4, x = 7π/4

49.

a)

A

b)

B

c)

C

d)

D

50.

Identify the Law of Sines. #1

a)

$\sin^2x+\cos^2x=1$

b)

$\frac{\sin\left(A\right)}{a}=\frac{\sin\left(B\right)}{b}=\frac{\sin\left(C\right)}{c}$

c)

$\sin\left(A\right)\sin\left(B\right)\sin\left(C\right)=1$

d)

Soh Cah Toa

51.

Use the Law of Sines to solve for BC. #2

a)

33

b)

24

c)

12

d)

29

52.

Calculate the length of AC. #4

a)

30

b)

24

c)

27

d)

35

53.

Find the length of BC. #7

a)

A

b)

B

c)

C

d)

D

54.

What are the possible criteria for Law of Sines? #14

a)

SSA, ASA, AAS

b)

AAS, SSS, ASA

c)

SAS, SSS, ASA

d)

SAS, AAS, ASA

55.

Which equation shows how you would use the law of sines to find side c? #8

a)

$\frac{\sin41}{19}=\frac{\sin\ 75}{c}$

b)

$\frac{\sin\ 64}{19}=\frac{\sin\ 75}{c}$

c)

$\frac{\sin\ 19}{64}=\frac{\sin\ c}{75}$

d)

$\frac{\sin19}{41}=\frac{\sin\ c}{75}$

56.

Find AB. #3

a)

10

b)

8

c)

6.1

d)

4.9

57.

What is the measure of angle A? #10

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

58.

Which equation shows how you would use the law of sines to find angle A? #11

a)

$\frac{\sin44}{26}=\frac{\sin\ A}{23}$

b)

$\frac{\sin\ 26}{44}=\frac{\sin\ 23}{A}$

c)

$\frac{\sin\ 44}{23}=\frac{\sin\ A}{26}$

d)

$\frac{\sin23}{44}=\frac{\sin\ 26}{A}$

59.

Without constructing the triangle, say how many possible triangles there are if: $A=100^0,\ a=7,b=5$

a)

0

b)

1

c)

2

d)

3

60.

Without constructing the triangle, say how many possible triangles there are if: $B=50^0,\ c=5,\ b=3$

a)

0

b)

1

c)

2

d)

3

61.

Without constructing the triangle, say how many possible triangles there are if: $C=67^0,\ c=4,\ b=3$

a)

0

b)

1

c)

2

d)

3

62.

Without constructing the triangle, say how many possible triangles there are if: $A=35^0,\ a=3,\ c=4$

a)

0

b)

1

c)

2

d)

3

63.

$A=56^0,\ b=3,\ c=6$

You can use the Law of Sines to solve the following triangle:

a)

Yes

b)

No

64.

Determine the number of possible triangles that can be drawn with the following dimensions: m<B = 33, a=27, and b = 22.

a)

0

b)

1

c)

2

d)

3

65.

Determine the number of possible triangles that can be drawn with the following dimensions: m<B = 29, a = 14 and b = 19.

a)

0

b)

1

c)

2

d)

3

66.

Determine the number of possible triangles that can be drawn with the following dimensions: m<A = 29, c = 18, and a = 17

a)

0

b)

1

c)

2

d)

3

67.

Based on the given information determine the number of unique triangles that may exist.
B= 70°, b=85, c=88

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

68.

Based on the given information determine the number of unique triangles that may exist.
A= 37°, a=8, b=14

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

69.

Based on the given information determine the number of unique triangles that may exist.
J = 98°, j = 29, p = 6

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

70.

3. How many triangles does the following form?

B=124°

a=1

b=2

a)

0

b)

1

c)

2

d)

Infinite

71.

How many triangles can you make if A=53, b=6, and a=5?

a)

0

b)

1

c)

2

d)

Infinitely many

72.

Two stakes are holding a small blimp in place. Stake A measures an angle of elevation of 49o and Stake B measures an angle of elevation of 58o. If the string attached to Stake A has a length of 148 feet, what is the length of the string attached to Stake B? (a)

Choose from the below words

152.7 feet

166.3 feet

157.3 feet

131.7 feet

73.

Which law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

74.

Which law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

75.

Which law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

76.

For which triangle would you use Law of Sines?

a)

b)

c)

d)

77.

To approximate the length of a marsh, a surveyor walks 425 meters from point A to point B. Then the surveyor turns 65º and walks 300 meters to point C. Approximate the length AC of the marsh.

a)

250 m

b)

615 m

c)

500 m

d)

790 m

78.

Which angle should you solve first using the Law of Cosines? (a)

Choose from the below words

Angle A

Angle B

Angle C

It doesn't matter

79.

What are the possible criteria for Law of Sines? (a)

Choose from the below words

SSA, ASA, AAS

AAS, SSS, ASA

SAS, SSS, ASA

SAS, AAS, ASA

80.

What are the possible criteria for the Law of Cosines? (a)

Choose from the below words

SSA, SSS

SSA, ASA

SSS, SAS

AAS, ASA

81.

Which set of given information shows the ambiguous case. (a)

Choose from the below words

AAS

SAS

SSA

SSS

82.

Find $m\angle\ A$ (a)

Choose from the below words

D

A

B

C

83.

Which Law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

84.

Which Law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

85.

Which Law would you use? (a)

Choose from the below words

Law of Sines

Law of Cosines

86.

Find the length of side AB.

87.

Find the length of side AC.

88.

What is the measure of angle A? (a)

Choose from the below words

50 degrees

60 degrees

78 degrees

74 degrees

89.

Find BC (a)

Choose from the below words

A

B

C

D

90.

Amanda and Jamie are standing 30 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 50 degrees, and from Jamie to the bird is 60 degrees. How far away, to 2 decimal places, is the bird from Amanda? (a)

Choose from the below words

33.92 ft

27.65 ft

24.46 ft

36.80 ft

91.

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle. To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart, to three decimal places, should the footings for each A-frame be? (a)

Choose from the below words

5.461 feet

9.743 feet

58.579 feet

7.654 feet

92.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

SAS

b)

SSS

c)

ASA

d)

HL

93.

Which triangle congruence theorem can be used to prove the triangles are congruent?

a)

SSS

b)

ASA

c)

AAS

d)

SAS

94.

$Which\ of\ the\ following\ guarantees\ that\ \Delta FAI\ \cong\ \Delta FRI\ ?$

a)

SSS Postulate

b)

SAS Postulate

c)

ASA Postulate

d)

AAS Theorem

95.

Equilateral

a)

All sides and all angles are congruent

b)

2 sides and 2 angles are congruent

c)

All sides and all angles are NOT congruent

d)

Angles are all less than 90 degrees

96.

Isosceles

a)

All sides and all angles are congruent

b)

2 sides and 2 angles are congruent

c)

All sides and all angles are NOT congruent

d)

Angles are all less than 90 degrees

97.

In a right triangle, one angle has to be (a)

Choose from the below words

90

180

60

45

98.

Using the law of sines, which expression is equivalent to $\frac{b}{\sin\ B}$ ?

a)

$\frac{a}{\sin\ A}$

b)

$\frac{a}{c}$

c)

$\frac{\sin\ A}{a}$

d)

$\frac{c}{\sin A\ }$

99.

The law of sines cannot be used to solve a triangle if

a)

three sides are given.

b)

two angles and a side are given.

c)

the given triangle is a right triangle.

d)

two sides and an angle opposite one of them are given.

100.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

101.

Find angle Z

a)

20.15°

b)

71.23°

c)

51.06°

d)

57.71°

102.

Use Law of Cosines to find angle T

a)

62.2°

b)

53.1°

c)

59.5°

d)

64.7°

103.

Find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

104.

Find QR

a)

34.7 km

b)

2.2 km

c)

13.74

d)

31.1 km

105.

Find the missing side.

a)

15.9 in.

b)

22.8 in.

c)

19.2 in.

d)

521.1 in.

106.

A GPS satellite measures the distances to two buildings to be 370 km and 350 km, and the angle between them to be 2.1^o (see diagram). How far apart are the two buildings?

a)

17.90 km

b)

30.32 km

c)

15.61 km

d)

23.96 km

107.

Solve the Triangle B= 85°, C= 47°, and a=19 Find A, b, and c

Answer: A = (a)

b = (b)

c = (c)

Choose from the below words

$48\degree$

$25.5$

$18.7$

$39\degree$

$90\degree$

$14$

$23.6$

$23.4$

$90\degree$

$32\degree$

108.

Will this make 1 triangle? 2 Triangles? or No Triangles?
B= 70°, b=85, c=88

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

109.

Will this make 1 triangle? 2 triangles? or no triangles?
A= 37°, a=8, b=14

a)

1 Trianlge

b)

2 Triangles

c)

No Triangles

110.

In triangle ABC, a = 3, b = 5, c = 7. What is the measure of the largest angle?

a)

22

b)

38

c)

60

d)

120

111.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

*Type your answer to the nearest TENTH

*Don't forget your UNITS!

(a)

112.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

*Type your answer to the nearest TENTH

*Don't forget your UNITS!!

(a)

113.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

114.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

115.

What would be used to find the distance from the Ranger's Tower to the fire?

a)

Quadratic Formula

b)

Law of Cosines

c)

Law of Sines

d)

Trigonometric Ratios

116.

What would be used to find the distance across the lake?

a)

Quadratic Formula

b)

Law of Cosines

c)

Law of Sines

d)

Trigonometric Ratios

117.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

118.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

119.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

Precalc Test 10 - Trig Equations

Total questions: 119

Worksheet time: 8hrs 18mins

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