Deck 6: Equations

Question 1

If a projectile (such as a bullet)is fired into the air with an initial velocity v at an angle of elevation θ  (see the figure), then the height h of the projectile at time t is given by h = -16 t ² + vt sin  θ Give the equation for the height, if v is 1,600 feet per second and θ  is 30°. (Leave your answer in exact value form.)
​

A)
B)
C)
D)
E)

Answer 1

Question 2

Solve the equation for t if . Give the answer as an exact value in radians. Do not use a calculator. ​

A) , 
B) , 
C) , 
D) , 
E) , 

Answer 2

, 

Question 3

Solve the equation for θ  if . Do not use a calculator.

Answer 3

150°, 210°

Question 4

Use the quadratic formula to find all solutions in the interval  to the nearest tenth of a degree. ​

A)15.9°, 163.3°
B)16.1°, 163.5°
C)16.1°, 163.7°
D)16.3°, 163.7°
E)16.3°, 163.5°

Question 5

Find all solutions in the interval . Use a calculator on the last step and write all answers to the nearest tenth of a degree. 4sin  θ - 8 = 5sin  θ - 4
​

A)250.5°, 289.5°
B)19.5°, 340.5°
C)70.5°, 340.5°
D)199.5°, 340.5°
E)

Question 6

Solve the equation for θ  if . Do not use a calculator. ​

A)120°; 240°
B)150°; 330°
C)60°; 240°
D)45°; 225°
E)30°; 120°

Question 7

Find all degree solutions to the equation. ​

A)20° + 90° k , 50 ° + 90 ° k
B)50° + 90 ° k , 65 ° + 90 ° k
C)20° + 90 ° k , 70 ° + 90 ° k
D)40° + 90 ° k , 50 ° + 90 ° k
E)40° + 90 ° k , 70 ° + 90 ° k

Question 8

Solve the equation for θ  if . Do not use a calculator.

Question 9

Solve the equation for θ  if . Do not use a calculator.
2cos  θ + 1 = 0
​

A)60°; 120°
B)45°; 315°
C)120°; 240°
D)60°; 300°
E)45°; 45°

Question 10

Use your graphing calculator to find the solutions to the equation to the nearest tenth of a degree in the interval  by defining the left side and right side of the equation as functions and then finding the intersection points of their graphs. Make sure your calculator is set to degree mode. sin  θ  - 4 = 6sin  θ
​

A)233.4°, 306.6°
B)233.1°, 306.6°
C)233.7°, 306.3°
D)233.1°, 306.9°
E)233.4°, 306.9°

Question 11

Solve for x , if . Write your answers in exact values only. sin x + 2sin x cos x = 0
​

A) ,  ,  , 
B)0,  ,  , 
C) ,  ,  , 
D) ,  ,  , 
E)0,  ,  , 

Question 12

Solve for θ  if . ​

A)60°, 300°
B)30°, 330°
C)30°, 150°
D)210°, 330°
E)240°, 300°

Question 13

Solve for θ  if . ​

A)60°, 300°
B)240°, 300°
C)30°, 330°
D)60°, 120°
E)120°, 240°

Question 14

Solve the equation for t  if . Give the answer as an exact value in radians. Do not use a calculator.

Question 15

Solve the equation for θ  if . Do not use a calculator.

Question 16

Solve the equation for θ  if . Do not use a calculator. ​

A)120°; 300°
B)30°; 210°
C)60°; 240°
D)150°; 240°
E)45°; 225

Question 17

Solve for x , if . Write your answers in exact values only. ​

A) ,  , 
B)0 ,  , 
C) ,  , 
D)0 ,  , 
E)0 ,  , 

Question 18

Solve the equation for θ  if . Do not use a calculator.

Question 19

Solve the equation for θ  if . Do not use a calculator. ​

A)60°; 300°
B)150°; 330°
C)30°; 210°
D)135°; 315°
E)120°; 300°

Question 20

Solve the equation for θ  if . Do not use a calculator.

Question 21

Solve the equation for θ  if . Give your answer in degrees. sin 2 θ + cos  θ = 0
​

A)90 ° , 210 ° , 270 ° , 330°
B)30 ° , 90 ° , 150 ° , 270 °
C)0 ° , 120 ° , 180 ° , 240 °
D)210 ° , 330 °
E)0 ° , 60 ° , 180 ° , 300 °

Question 22

Solve the equation for x if . ​

A) ,  , 
B)0,  , 
C) ,  , 
D) , , 
E) ,  , 

Question 23

Solve the equation for θ  if . Give your answer in degrees. ​

A)0°
B)30°, 150°
C)90°, 180°
D)0°, 180°
E)240°, 300°

Question 24

Solve the equation for x  if . cos x - cos 2 x = 0
​

A) ,  , 
B) ,  , 
C) ,  , 
D)0,  , 
E) ,  , 

Question 25

Solve for x , if . Write your answers in exact values only.

Question 26

Solve the equation for x if . ​

A) , 
B) , 
C) , 
D) , 
E) ,  , 

Question 27

Solve for x , if . Write your answers in exact values only.

Question 28

Solve the equation for θ  if . Do not use a calculator.

Question 29

Solve the equation for t  if . Give the answer as an exact value in radians. Do not use a calculator.

Question 30

Solve the equation for t  if . Give the answer as an exact value in radians. Do not use a calculator.

Question 31

Solve the equation for x if . ​

A)0,  , 
B) , , 
C)0,  , 
D) ,  , 
E) ,  , 

Question 32

Use your graphing calculator to find the solutions to the equation to the nearest tenth of a degree in the interval  by defining the left side and right side of the equation as functions and then finding the intersection points of their graphs. Make sure your calculator is set to degree mode.
sin  θ - 4 = 7sin  θ

Question 33

Solve for θ  if .

Question 34

Solve the equation for θ  if . Give your answer in degrees. ​

A)240°, 300°
B)225°, 315°
C)120°, 240°
D)60°, 120°
E)45°, 135°

Question 35

If a projectile (such as a bullet)is fired into the air with an initial velocity v at an angle of elevation θ  (see the figure), then the height h of the projectile at time t is given by Give the equation for the height, if v is 1,800 feet per second and θ  is 30°. (Leave your answer in exact value form.)

Question 36

Use the quadratic formula to find all solutions in the interval  to the nearest tenth of a degree.

Question 37

Solve for x , if . Write your answers in exact values only.

Question 38

Solve the equation for x if . ​

A) , 
B) , 
C) ,  , 
D) , 
E) , 

Question 39

Solve the equation for θ  if . Give your answer in degrees. ​

A)0°, 120 ° , 240 °
B)30 ° , 150 ° , 270 °
C)90 ° , 210 ° , 330 °
D)60 ° , 180 ° , 300 °
E)150 ° , 180 ° , 210 °

Question 40

Solve for θ  if .

Question 41

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 42

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 43

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 44

Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree. ​

A)201.5°, 338.5°
B)202.1°, 337.9°
C)201.9°, 338.1°
D)200.7°, 339.3°
E)201.7°, 338.3°

Question 45

Solve the equation for θ  if . ​

A)60 ° , 300°
B)210 °
C)0 ° , 240 °
D)330 °
E)120 °

Question 46

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 47

Solve the equation for θ  if . ​

A)60°, 300°
B)0°, 300°
C)60°, 120°
D)90°, 150°
E)180°, 240°

Question 48

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 49

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 50

Use your graphing calculator to find all radian solutions in the interval  for the following equation. Round your answers to four decimal places. ​

A)3.5931, 5.8317
B)3.5933, 5.8315
C)3.5937, 5.8311
D)3.5933, 5.8317
E)3.5931, 5.8315

Question 51

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 52

Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree. ​

A)65.1°, 294.9°
B)65.7°, 294.3°
C)66.5°, 293.5°
D)65.3°, 294.7°
E)65.5°, 294.5°

Question 53

Find all degree solutions for the equation  in the interval . ​

A)14.5°, 23.8°, 156.2°, 165.5°
B)14.5°, 23.6°, 156.4°, 165.5°
C)14.7°, 23.8°, 156.2°, 165.3°
D)14.1°, 23.2°, 156.8°, 165.9°
E)14.7°, 23.6°, 156.4°, 165.3°

Question 54

Find all degree solutions for the equation  in the interval . ​

A)33.9°, 146.1°, 213.9°, 326.1°
B)34.1°, 145.9°, 214.1°, 325.9°
C)33.7°, 146.3°
D)33.9°, 146.1°
E)33.7°, 146.3°, 213.7°, 326.3°

Question 55

Write an expression that gives all solutions to the equation. ​

A)
B)
C)
D)
E)

Question 56

Solve the equation for θ  if . ​

A)30°, 90°
B)30°, 330°
C)210°, 270°
D)0°, 60°
E)150°, 210°

Question 57

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 58

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 59

Solve the equation for x  if . Give your answer in radians using exact values only.

Question 60

Write an expression that gives all solutions to the equation. ​

A)
B)
C)
D)
E)

Question 61

Find all solutions if . Verify your answer graphically. ​

A)45°, 135 °
B)15 ° , 75 ° , 195 ° , 255 ° , 280 °
C)30 ° , 60 ° , 210 ° , 240 °
D)15 ° , 75 ° , 195 ° , 255 °
E)30 ° , 60 ° , 210 ° , 240 ° , 260 °

Question 62

Find all solutions if . Use exact values only. ​

A) ,  ,  ,  ,  , 
B) ,  ,  ,  ,  , 
C)0,  ,  ,  ,  , 
D) ,  ,  ,  ,  , 
E) ,  , 

Question 63

Solve the equation for θ  if . Give your answer in degrees.

Question 64

Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree.

Question 65

Use your graphing calculator to find all radian solutions in the interval  for the following equation. Round your answers to four decimal places.

Question 66

Solve the equation for θ  if . Give your answer in degrees.

Question 67

For the equation below, find all degree solutions in the interval . Give your answer in degrees. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify each solution graphically.

Question 68

Solve the equation for θ  if . Give your answer in degrees.

Question 69

Write an expression that gives all solutions to the equation. -

Question 70

Solving the following equation will require you to use the quadratic formula. Solve the equation for θ  between 0° and 360°, and round your answers to the nearest tenth of a degree.

Question 71

Solve the equation for θ  if . Give your answer in degrees.

Question 72

Find all solutions if . Use exact values only. Verify your answer graphically. ​

A) ,  ,  , 
B) ,  ,  , 
C) ,  ,  , 
D) ,  ,  , 
E)0, 

Question 73

Solve the equation for θ  if . Give your answer in degrees.

Question 74

Find all degree solutions for the following. ​

A)  or 
B)  or 
C)  or 
D)
E)  or 

Question 75

Solve the equation for θ  if . Give your answer in degrees.

Question 76

Solve the equation for θ  if . Give your answer in degrees.

Question 77

For the equation below, find all degree solutions in the interval . Give your answer in degrees. If rounding is necessary, round to the nearest tenth of a degree. Use your graphing calculator to verify each solution graphically.

Question 78

Use your graphing calculator to find all degree solutions in the interval  for the following equation. ​

A)15°, 105 ° , 135 ° , 225 ° , 255 ° , 345 °
B)10 ° , 110 ° , 130 ° , 230 ° , 250 ° , 350 °
C)60 ° , 180 ° , 300 °
D)30 ° , 90 ° , 150 ° , 210 ° , 330 °
E)20 ° , 100 ° , 140 ° , 220 ° , 260 ° , 340 °

Question 79

Write an expression that gives all solutions to the equation. 00

Question 80

Find all solutions in radians using exact values only. ​

A)  or 
B)  or 
C)
D)  or 
E)  or