Deck 1: The Six Trigonometric Functions

Question 1

Give the complement and the supplement of angle  z .  ​

A)Complement: 90° -  z  Supplement: 90° +  z
B)Complement: 180° -  z  Supplement: 90° -  z
C)Complement: 90° -  z  Supplement: 180° -  z
D)Complement: - z  Supplement: 180° -  z
E)Complement: 90° +  z  Supplement: 90° -  z

Answer 1

Complement: 90° -  z  Supplement: 180° -  z

Question 2

Indicate if the angle 50° is acute or obtuse. Then give the complement and the supplement of the angle. ​

A)obtuse; complement: 040° supplement: 130°
B)acute; complement: 040 ° supplement: 130 °
C)acute; complement: 040° supplement: -50°
D)obtuse; complement: 040° supplement: -50°
E)acute; complement: 130° supplement: 040°

Answer 2

acute; complement: 040 ° supplement: 130 °

Question 3

The figure shows a walkway with a handrail. Angle α  is the angle between the walkway and the horizontal, while angle  β  is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal. Find α  if β = 52°.

A)α = 57°
B)α  = 123 °
C)α  = 38 °
D)α  = 128 °
E)α  = 52 °

Answer 3

α  = 38 °

Question 4

An escalator in a department store is to carry people a vertical distance of 25 feet between floors. How long is the escalator if it makes an angle of 30° with the ground? ​

A)42 feet
B)31 feet
C)41 feet
D)50 feet
E)39 feet

Question 5

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.

A) , 
B) , 
C)​ , 
D) , 
E) , 

Question 6

Find β  if B = 4 β . Remember: The sum of the three angles in any triangle is always 180°.

A)β = 72°
B)β  = 19 °
C)β  = 21 °
D)β  = 18 °
E)β  = 69 °

Question 7

Suppose ABC  is a right triangle with C = 90°. If a = 6 and c = 10, find b . ​

A)b = 9
B)b  = 13
C)b  = 8
D)b  = 4
E)b  = 10

Question 8

Solve for x . , b = 1 ​

A)x = 1
B)x  = 7
C)x  = 3
D)x  = 5
E)x  = 4

Question 9

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of diagonal CF  in the figure is feet. What is the length of edge  AC ? ​

A)5 inches
B)  inches
C)  inches
D)  inches
E)  inches

Question 10

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 60°, what is the measure of the base angles?

A)50°
B)60°
C)45°
D)80°
E)65°

Question 11

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each ​

A)
B)
C)
D)
E)

Question 12

Suppose ABC  is a right triangle with C = 90°. If a = 6 and b = 8, find c .

A)c = 9
B)c  = 18
C)c  = 10
D)c  = 15
E)c  = 6

Question 13

Find r  if AB = 32 and AD = 40. ​

A)r = 14
B)r  = 10
C)r  = 9
D)r  = 7
E)r  = 5

Question 14

Find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 10. ​

A) , 
B)4, 
C)3, 
D)5, 
E) , 

Question 15

The object shown in the figure is a cube (all edges are equal in length). If the length of each edge of the cube shown in the figure is 1 inch0, find the length of diagonal CE . ​

A)  inches
B)  inch0
C)  inches
D)  inches
E)  inches

Question 16

Find A  if B = 20° and  α +  β = 120°. Remember: The sum of the three angles in any triangle is always 180°.

A)A = 60°
B)A  = 50 °
C)A  = 70 °
D)A  = 100 °
E)A  = 40 °

Question 17

Find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 4.

A) , 
B) , 
C) , 
D)​ , 
E) , 

Question 18

Solve for x . a = 5,  ​

A)x = 9
B)x  = 4
C)x  = 6
D)x  = 5
E)x  = 7

Question 19

A searchlight rotates through one complete revolution every 6 seconds. How long does it take the light to rotate through 300°? ​

A)4 sec.
B)7 sec.
C)2 sec.
D)3 sec.
E)5 sec.

Question 20

Find AB  if BC = 3, BD = 5, and AD = 6. ​

A)
B)
C)
D)
E)

Question 21

A searchlight rotates through one complete revolution every 2 seconds. How long does it take the light to rotate through 180°? __________ sec.

Question 22

Find A  if B = 20° and  α +  β = 100°. Remember: The sum of the three angles in any triangle is always 180°. A = __________°

Question 23

Find r  if AB = 18 and AD = 30.

Question 24

Solve for x . a = 2,

Question 25

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

Question 26

Find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 15.

Question 27

Suppose ABC  is a right triangle with C = 90°. If a = 15 and b = 8, find c .

Question 28

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 9.

Question 29

The object shown in the figure is a cube (all edges are equal in length). Suppose the length of the diagonal AH  in the figure is feet. What is the length of edge AB ?

Question 30

An escalator in a department store is to carry people a vertical distance of 19 feet between floors. How long is the escalator if it makes an angle of 30ᵒ with the ground? __________ feet.

Question 31

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 40°, what is the measure of the base angles? __________°

Question 32

Indicate if the angle 100° is acute or obtuse. __________
Give the complement angle. __________°
Give the supplement angle. __________°

Question 33

Find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 20.

Question 34

Solve for x .

Question 35

Find AB  if BC = 3, BD = 5, and AD = 7. Simplify the answer. Do not convert to decimal form.

Question 36

Give the complement angle of angle x . __________
Give the supplement angle of angle x . __________

Question 37

Suppose ABC  is a right triangle with C = 90°. If a = 12 and c = 15, find b .

Question 38

Find  α  if A  = α . Remember: The sum of the three angles in any triangle is always 180°. α = __________°

Question 39

Graph the following circle.

A)​ 
B)​ 
C)​ 
D)​
E)​

Question 40

The figure shows a walkway with a handrail. Angle α  is the angle between the walkway and the horizontal, while angle  β  is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal. Find  α  if  β = 55°. α = __________°

Question 41

Graph the parabola. ​

A)​ 
B)​ 
C)​ 
D)​
E)​

Question 42

Graph the ordered pair on a rectangular coordinate system: ​

A)​ 
B)​
C)​ 
D)​ 
E)​ 

Question 43

An airplane is approaching Los Angeles International Airport at an altitude of 5,280 feet. If the horizontal distance from the plane to the runway is 2.4 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (see the figure below). (5,280 feet equals 1 mile.) a = 2.4 miles, b = 5,280 feet __________ miles

Question 44

There is an angle in standard position whose terminal side contains the point . Find the distance from the origin to this point. ​

A)
B)33
C)
D)
E)11

Question 45

Find the distance between the points: , 

Question 46

Use the diagram to help you name an angle between 0° and 360° that is coterminal with the angle -120°. ​

A)-120 °
B)235°
C)240°
D)-240 °
E)120°

Question 47

Graph the circle with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x -coordinate. Write your answers as ordered pairs and round to four places past the decimal point when necessary.

Question 48

Find the distance between the points: , 

Question 49

Find x so the distance between and is

A)
B)
C)
D)
E)

Question 50

Graph the line. ​

A)​ 
B)​ 
C)​ 
D)​ 
E)​ 

Question 51

Use the diagram to help you name an angle between 0° and 360° that is coterminal with the angle -60°. __________°

Question 52

Find x so the distance between and is x = __________

Question 53

For points  in quadrant IV, the ratio  is always negative because x is always positive and y is always negative. In what other quadrant is the ratio  always negative?

Question 54

Find the distance between the points: , ​ ​

A)
B)
C)
D)
E)

Question 55

An airplane is approaching Los Angeles International Airport at an altitude of 10,560 feet. If the horizontal distance from the plane to the runway is 2.1 miles, use the Pythagorean Theorem to find the diagonal distance from the plane to the runway (see the figure below). (5,280 feet equals 1 mile.) a = 2.1 miles, b = 10,560 feet

A)2.6 miles
B)2.2 miles
C)2.9 miles
D)2.3 miles
E)2.8 miles

Question 56

Find the distance between the following points: ,  ​

A)3
B)5
C)4
D)2
E)1

Question 57

Graph the circle with your graphing calculator. Use the feature on your calculator that allows you to evaluate a function from the graph to find the coordinates of all points on the circle that have the given x-coordinate. ​

A) , 
B) , 
C) , 
D)
E) , 

Question 58

For points in quadrant IV, the ratio is always negative because x is always positive and y is always negative. In what other quadrant is the ratio always negative?  ​

A)quadrant I
B)quadrant VI
C)quadrant III
D)quadrant II
E)none of the above

Question 59

Name a point on the terminal side of 240°.

A)
B)
C)
D)
E)

Question 60

Which of the following angles are coterminal with -  45°?

A)0405°
B)045°
C)0315°
D)-  315°
E)-  405°

Question 61

Draw the following angle in standard position and then name the reference angle. ​

A)​ ​   ​
B)​    ​   ​
C)​ ​ ​
D)​    ​
E)​   ​

Question 62

In the diagram below, angle θ  is in standard position. Find , and ​

A) , ,
B)​ , ,
C)​​ , ,
D)​ , ,
E)​ , ,

Question 63

Find all six trigonometric functions of θ  if the given point is on the terminal side of θ .(Assume that a is a positive number.) ​

A) ;  ;  ;  ; 
B) ;  ;  ;  ; 
C) ;  ;  ;  ; 
D) ;  ;  ;  ; 
E) ;  ;  ;  ; 

Question 64

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below. ​

A)​   ​ , ,
B)​   ​ , ,
C)​   ​ , ,
D)​   ​ , ,
E)​   ​ , ,

Question 65

Indicate the quadrant(s)in which the terminal side of θ  must lie in order that cos  θ  is positive and tan  θ  is positive.

Question 66

Find sin  θ  and tan  θ  if the terminal side of θ  lies along the line  in quadrant I. ​

A) , 
B) , 
C) , 
D) , 
E) , 

Question 67

Find all six trigonometric functions of θ  if the given point is on the terminal side of θ . ​

A) ;  ;  ;  ; 
B) ;  ;  ;  ; 
C) ;  ;  ;  ; 
D) ;  ;  ;  ; 
E) ;  ;  ;  ; 

Question 68

In which quadrant must the terminal side of θ  lie if sin θ  and cot  θ  are to have the different sign? ​

A)IV
B)II and III
C)I and IV
D)I and II
E)III and IV

Question 69

Find the remaining trigonometric functions of θ  if  and θ  terminates in QII. ​

A)​ , , ,  ​ ,
B)​ , , , , ​
C)​ , , , , ​
D)​ , , , , ​
E) , , , ,

Question 70

Find y if the point (8, y )is on the terminal side of θ  and

A)y = 4
B)y  = ±6
C)y  = ±10
D)y  = 24
E)y  = ±15

Question 71

Find an angle θ  in the second quadrant for which cot  θ = - 1. Look for an angle between 0° and 360°. __________

Question 72

Find the remaining trigonometric functions of θ  if and cos  θ

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

Question 73

Find the remaining trigonometric functions of θ  if  and θ  terminates in QII. ​

A)​ , , , ,
B) , , , ,
C)​ , , , ,
D)​ , , , ,
E) , , , ,

Question 74

Find the remaining trigonometric functions of θ  if  where m and n are both positive. Assume that θ  is between 0° and 180°.

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

Question 75

Use your calculator to find sin  θ  and cos  θ  if the point  is on the terminal side of θ . ​

A)sin  θ = 0.8, cos  θ = 0.6
B)sin  θ  = 0.6, cos  θ  = 0.8
C)sin  θ  = 0.6, cos  θ  = -0.8
D)sin  θ  = -0.6, cos  θ  = -0.8
E)sin  θ  = -0.6, cos  θ  = 0.8

Question 76

Find an angle θ  in the fourth quadrant for which tan  θ = - 1 . Look for an angle between 0° and 360°. ​

A)300°
B)225°
C)120°
D)330°
E)315°

Question 77

Find all six trigonometric functions of θ  if the given point is on the terminal side of θ . ​

A)sin  θ = 0;  cos  θ  = 01;  csc  θ  = undefined sec  θ  = 01; tan  θ  = 0; cot  θ  = undefined
B)sin  θ  = 01;  cos  θ  = 0;  csc  θ  = 01 sec  θ  =  undefined ; tan  θ  = 0; cot  θ  = undefined
C)sin  θ  = 01;  cos  θ  = 0;  csc  θ  = 01 sec  θ  =  undefined ; tan  θ  = undefined ; cot  θ  = 0
D)sin  θ  = 0;  cos  θ  = 01;  csc  θ  = undefined sec  θ  = 01; tan  θ  = undefined ; cot  θ  = 0
E)sin  θ  = 01;  cos  θ  = 0;  csc  θ  = undefined sec  θ  = 01; tan  θ  = 0; cot  θ  = undefined

Question 78

Indicate the quadrants in which the terminal side of θ  must lie in order that sin  θ  is positive and tan  θ  is negative. ​

A)III
B)I
C)II
D)IV
E)none of the above

Question 79

Use your calculator to find sin  θ  and cos  θ  if the point is on the terminal side of  θ .
sin θ = __________
cos θ = __________

Question 80

Draw the following angle in standard position; find the sine, the cosine, and the tangent of the angle below. ​

A)​   ​ , ,
B)​   ​ , ,
C)​   ​ , ,
D)​   ​ , ,
E)​   ​ , ,