Deck 2: Right Triangle Trigonometry

Question 1

For expression , replace z with 90°, and then simplify as much as possible. ​

A)
B)​
C)​
D)​
E)​

Answer 1

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Question 2

Use the Cofunction Theorem to fill in the blank so that the expression becomes a true statement. _____ ​

A)
B)​
C)​
D)​
E)​

Answer 2

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Question 3

Find cos A in the right triangle below. ​

A)
B)​
C)​
D)​
E)​

Answer 3

Question 4

Find the exact value of . ​

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B)
C)
D)
E)

Question 5

Simplify the following expression by first substituting values from the table of exact values and then simplifying the resulting expression. ​

A)
B)​
C)​
D)​
E)​

Question 6

In the diagram below, angle A is in standard position. Find sin A . ​
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A)
B)​
C)​
D)​
E)​

Question 7

Find the exact value for csc 60°. ​

A)
B)​
C)​
D)​
E)​

Question 8

Find the exact value of . ​

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B)
C)
D)
E)

Question 9

In the diagram below, angle A is in standard position. Find sin A . ​
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A)
B)​
C)​
D)​
E)​

Question 10

Which of the following tables has been completed correctly using exact values? ​

A)
B)
C)
D)
E)

Question 11

Use the Cofunction Theorem to fill in the blank so that the expression becomes a true statement. _____° ​

A)
B)​
C)​
D)​
E)​

Question 12

Right triangle ABC  has , , and . Use this information to find cos A ​

A)
B)​
C)​
D)​
E)​

Question 13

For the expression that follows, replace x with 30°, and then simplify as much as possible. ​

A)
B)​
C)​
D)​
E)​

Question 14

Right triangle ABC  has , , and . Use this information to find sin A . ​

A)
B)​
C)​
D)​
E)​

Question 15

Find tan B in the right triangle below . ​

A)
B)​
C)​
D)​
E)​

Question 16

Find the exact value of sec 45°. ​

A)​
B)​
C)​
D)​
E)

Question 17

Find tan A in the right triangle below . ​

A)
B)​
C)​
D)​
E)​

Question 18

Simplify the following expression by first substituting values from the table of exact values and then simplifying the resulting expression.

A)
B)
C)1
D)0
E)

Question 19

There is a right triangle ABC with , , and  Use a calculator to find cos A . Round your answer to the nearest hundredth. ​

A)0.87
B)0.86
C)0.48
D)0.49
E)0.85

Question 20

Which of the following tables has been completed correctly using exact values? ​

A)
B)​
C)
D)
E)

Question 21

Use the Cofunction Theorem to fill in the blank so that the expression becomes a true statement. _____°

Question 22

Simplify the following expression by first substituting values from the table of exact values and then simplifying the resulting expression.

Question 23

Add. (34°41')+  (23 °22 ' ) ​

A)23°03'
B)59°23'
C)59°03'
D)58°23'
E)58°03'

Question 24

Use the Cofunction Theorem to fill in the blank so that the expression becomes a true statement. _____

Question 25

Simplify the following expression by first substituting values from the table of exact values and then simplifying the resulting expression.

Question 26

There is a right triangle ABC with , , and . Use a calculator to find sin A , cos A , sin B , and cos  B . Round your answers to the nearest hundredth.
sin A = __________
cos A = __________
sin B = __________
cos B = __________

Question 27

Suppose each edge of the cube shown in the figure is 3 inches long. Find the sine and cosine of the angle formed by diagonals GB and 0 GD . ​

A)​
B)​
C)​
D)​
E)​

Question 28

Find the exact value of cot 60°.

Question 29

For the expression , replace z with , and then simplify as much as possible.

Question 30

Find the exact value for csc 60°.

Question 31

Convert the following to degrees and minutes. Round to the nearest minute. 91.15° ​

A)91°15'
B)91°14'
C)91°10'
D)91°9'
E)91°6'

Question 32

Subtract. (83°36')- (72°66') ​

A)10°30'
B)31°10'
C)10°31'
D)11°31'
E)30°10'

Question 33

Simplify the following expression by first substituting values from the table of exact values and then simplifying the resulting expression.

Question 34

For the expression that follows, replace x with 30°, and then simplify as much as possible.

Question 35

Find the exact value of sec 30°.

Question 36

Change the following to decimal degrees. 45°33' ​

A)46.65°
B)46.05°
C)44.85°
D)46.45°
E)45.55°

Question 37

Convert the following to degrees and minutes. Round to the nearest minute. 34.7° ​

A)34°37'
B)34°7'
C)34°41'
D)34°45'
E)34°42'

Question 38

Change the following to decimal degrees. 71°18' ​

A)70.8°
B)73.1°
C)72°
D)71.3°
E)72.3°

Question 39

There is a right triangle ABC with , , and . Use a calculator to find sin B . Round your answers to the nearest hundredth. ​

A)0.94
B)0.28
C)0.97
D)0.96
E)0.29

Question 40

There is a right triangle ABC with , , and . Use a calculator to find sin A , cos A , sin B , and cos B .  Round your answers to the nearest hundredth.
sin  A  = __________
cos  A  = __________
sin B = __________
cos B = __________

Question 41

To further justify the Cofunction Theorem, use your calculator to find a value for each pair of trigonometric functions below. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point. sin 23°, cos 67° ​

A)sin 23° = 0.3907, cos 67° = -0.9205
B)sin 23 ° = -0.3907 , cos 67 ° = 0.9205
C)sin 23 ° = 0.3977 , cos 67 ° = 0.9135
D)sin 23 ° = 0.3907 , cos 67 ° = 0.3907
E)sin 23 ° = 0.3857 , cos 67 ° = 0.9205

Question 42

Use a calculator to find a value of θ  between 0° and 90° that satisfies the statement below. Write your answer in degrees and minutes rounded to the nearest minute. cos  θ = 0.5673 ​

A)θ  = 55°026'
B)θ  = 54°028'
C)θ  = 54°026'
D)θ  = 55°028'
E)θ  = 53°026'

Question 43

Use a calculator to find the following. Round the answer to four places past the decimal point. cos 81.4°

Question 44

Use a calculator to find the following. Round your answer to four places past the decimal point. sin 25°30'

Question 45

Use a calculator to find the following. Round your answer to four places past the decimal point. sec 47.9° ​

A)1.5806
B)1.4246
C)1.4916
D)1.6366
E)1.3686

Question 46

Use a calculator to find the following. Round your answer to four places past the decimal point. cot 31° ​

A)1.5193
B)-1.6813
C)1.6643
D)1.4863
E)1.7873

Question 47

Use a calculator to find the following. Round the answer to four places past the decimal point. cot 36°

Question 48

Use a calculator to find the following. Round your answer to four places past the decimal point. sec 60°48'

Question 49

Use a calculator to find the following. Round your answer to four places past the decimal point. sec 41.2°

Question 50

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. cot  θ = 0.8536 ​

A)θ  = 49.4°
B)θ  = 48.0°
C)θ  = 49.5°
D)θ  = 52.3°
E)θ  = 50.6°

Question 51

Use a calculator to find the following. Round the answer to four places past the decimal point. cos 83.9° ​

A)0.0893
B)0.1063
C)0.1193
D)-0.1173
E)0.1293

Question 52

Use a calculator to find the following. Round your answer to four places past the decimal point. sin 25°40' ​

A)0.5561
B)0.6191
C)0.4331
D)0.4481
E)0.5781

Question 53

Use a calculator to find a value of θ  between 0° and 90° that satisfies the statement below. Write your answer in degrees and minutes rounded to the nearest minute. csc  θ = 4.1973 ​

A)θ  = 10°047'
B)θ  = 14°047'
C)θ  = 13°047'
D)θ  = 14°049'
E)θ  = 13°049'

Question 54

Use a calculator to complete the table of sin and csc values and determine which of the tables below displays the correct values. (Be sure your calculator is in degree mode.)Round all answers to four digits past the decimal point. If you have a graphing calculator with table-building capabilities, use it to construct the tables.

A)​
B)​
C)​
D)​
E)​

Question 55

Change the following to decimal degrees. If rounding is necessary, round to the nearest hundredth of a degree. 44°21' __________°

Question 56

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. sin  θ ​ = 0.6438 ​

A)θ = 42.2°
B)θ  = 41.4°
C)θ  = 40.1°
D)θ  = 40.0°
E)θ  = 41.6°

Question 57

Calculate the tangent values for each value of x indicated in the sets of tables shown below. Determine which set of tables displays the correct values. Round all answers to the nearest tenth. ​

A)​
B)​
C)​
D)​
E)​

Question 58

Work the following problem on your calculator. Do not write down or round off any intermediate answers. ​

A)1
B)0.3
C)0.6
D)3
E)0.4

Question 59

Change the following to decimal degrees. If rounding is necessary, round to the nearest tenth of a degree. 73°12' __________°

Question 60

Use a calculator to find the following. Round your answer to four places past the decimal point. sec 30°48' ​

A)1.2872
B)1.1642
C)1.0972
D)-0.9662
E)1.3182

Question 61

Refer to right triangle ABC with . ​ ​ If  mm and  mm, find B . Round the answer to the nearest whole number. ​

A)​
B)​
C)​
D)​
E)​

Question 62

Use a calculator to find a value of θ  between 0° and 90° that satisfies the statement below. Write your answer in degrees and minutes rounded to the nearest minute. csc  θ = 5.3187 θ =  _____°_____'

Question 63

Refer to right triangle ABC with . Solve for all the missing parts using the given information. Round the answers to the nearest tenth if necessary. ​

A)
B)​
C)​
D)​
E)​

Question 64

Convert the following to degrees and minutes. Round to the nearest minute. 32.8° _____°_____'

Question 65

Add. (34°46')+ (29°24')_____°_____'

Question 66

Refer to right triangle ABC with . If  and  cm, find b . Round the answer to the nearest whole number. ​

A)65 cm
B)64 cm
C)68 cm
D)67 cm
E)69 cm

Question 67

Convert the following to degrees and minutes. Round to the nearest minute. 93.65° _____°_____'

Question 68

Use a calculator to find a value of θ  between 0° and 90° that satisfies the statement below. Write your answer in degrees and minutes rounded to the nearest minute. cos  θ = 0.3145 θ =  _____°_____'

Question 69

Refer to right triangle ABC with . Solve for all the missing parts using the given information. Round the number of degrees, the number of minutes, and the lengths of the sides to the nearest whole number. ​

A)​
B)​
C)​
D)​
E)

Question 70

Complete each of the following tables. Round all answers to the nearest tenth.

Question 71

To further justify the Cofunction Theorem, use your calculator to find a value for each pair of trigonometric functions below. In each case, the trigonometric functions are cofunctions of one another, and the angles are complementary angles. Round your answers to four places past the decimal point. sin 28° = _____ , cos 62° = _____

Question 72

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. sin  θ = 0.6792 θ =  __________°

Question 73

Work each of the following problems on your calculator. Do not write down or round off any intermediate answers.  = __________  =  __________  =  __________  =  __________

Question 74

Refer to right triangle ABC with . ​ If  inches and  inches, find B .​ Round the answer to the nearest tenth. ​

A)
B)
C)
D)
E)

Question 75

Subtract. (86°34') - (25°64')_____°_____'

Question 76

Refer to right triangle ABC with . ​ ​ If  and  yd, find a . Round the answer to the nearest hundredth. ​

A)8.79 yd
B)8.85 yd
C)8.81 yd
D)8.75 yd
E)8.77 yd

Question 77

Refer to right triangle ABC with . Solve for all the missing parts using the given information. Round each answer to the nearest whole number. ​

A)​
B)​
C)​
D)​
E)​

Question 78

Use a calculator to complete the following table. (Be sure your calculator is in degree mode.)Round all answers to four digits past the decimal point. If you have a graphing calculator with table-building capabilities, use it to construct the tables.

Question 79

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. cot  θ = 0.7382 θ =  __________°

Question 80

Refer to right triangle ABC with . ​ If  and  cm, find b . Round the answer to the nearest hundredth. ​

A)2.12 cm
B)2.27 cm
C)2.18 cm
D)2.21 cm
E)2.33 cm