Deck 1: Trigonometric Functions

Question 1

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
160°

Answer 1

B

Question 2

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
( , ); Find tan ϴ.

Answer 2

D

Question 3

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.

Answer 3

B

Question 4

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
csc (° °)and cot (° °)

A)positive and positive
B)negative and negative
C)positive and negative
D)negative and positive

Answer 4

D

Question 5

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
csc ϴ, given that sin ϴ = -0.0214

A)23.365
B)46.729
C)-23.365
D)-46.729

Question 6

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
C

Question 7

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
(4, -2)

Question 8

The triangles are similar. Find the missing side, angle or value of the variable.

Question 9

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
(-2, 5)

Question 10

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
98°

Question 11

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
(18, 24); Find csc ϴ.

Question 12

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
B

Question 13

Identify the quadrant for the angle satisfying the following conditions.
cot ϴ > 0 and sin ϴ < 0

A)Quadrant I
B)Quadrant IV
C)Quadrant III
D)Quadrant II

Question 14

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
27° and 101°

A)128°
B)232°
C)38°
D)52°

Question 15

Solve the problem. Round answers to the nearest tenth if necessary.
A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.

A)75.5 m
B)18.7 m
C)17.2 m
D)77.0 m

Question 16

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
tan(n · 180°)

A)0
B)1
C)Undefined
D)-1

Question 17

Find the measure of each angle in the problem.
Complementary angles with measures 3x and 6x - 18 degrees

A)66° and 114°
B)12° and 78°
C)36° and 54°
D)38° and 52°

Question 18

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
(3, -6)

Question 19

Perform the calculation.
279°39´ + 139°38´

A)18°77´
B)18°17´
C)419°17´
D)419°77´

Question 20

Find the exact value of the expression.
B

Question 21

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.

Question 22

Use the fundamental identities to find the value of the trigonometric function.

Question 23

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
115°

Question 24

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
28°23' and 95°22'

A)236°55'
B)57°15'
C)56°15'
D)237°55'

Question 25

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
cos (500°)and tan (500°)

A)negative and negative
B)negative and positive
C)positive and positive
D)positive and negative

Question 26

Evaluate the expression.

Question 27

Use the fundamental identities to find the value of the trigonometric function.

Question 28

Find the measure of the third angle of a triangle if the measures of the other two angles are given.

Question 29

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.

A)Positive
B)Negative

Question 30

Convert the angle to degrees, minutes, and seconds.
102.5° and 42.4°

A)55.1°
B)35.1°
C)45.1°
D)215.1°

Question 31

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
tan((2n + 1)· 90°)

A)0
B)Undefined
C)-1
D)1

Question 32

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
(-4, 0)

Question 33

Identify the quadrant for the angle satisfying the following conditions.
22.66°

A)22°39´66´´
B)22°39´42´´
C)22°39´24´´
D)22°39´36´´

Question 34

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
(0, -5)

Question 35

Use the fundamental identities to find the value of the trigonometric function.

Question 36

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
951°

A)221°
B)581°
C)231°
D)591°

Question 37

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
x

Question 38

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
sin(-540)°

A)1
B)
C)-1
D)Undefined

Question 39

Use the fundamental identities to find the value of the trigonometric function.
AC

Question 40

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.

Question 41

Solve the problem.
badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from
geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that
cuts off the same arc. See the figure.) Answer: A
Explanation: A)
B)
C)
D)
10
The triangles are similar. Find the missing side, angle or value of the variable.
Determine the measure of the angle in each point of the six-pointed star appearing on police badges and vehicles. (Hint: Inscribe the star in a circle, and use the following theorem from geometry: An angle whose vertex lies on the circumference of a circle is equal to half the central angle that
Cuts off the same arc. See the figure.)

Question 42

Find the angle of least positive measure coterminal with the given angle.
cot ϴ, given that tan ϴ = 0.3355

A)2.974
B)2.988
C)2.995
D)2.981

Question 43

Find the angle of least positive measure coterminal with the given angle.
x and y

Question 44

Use the fundamental identities to find the value of the trigonometric function.

Question 45

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
20°

Question 46

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
-47°

A)43°
B)47°
C)313°
D)223°

Question 47

Use the properties of angle measures to find the measure of each marked angle.
BC

Question 48

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
57°25´27´´

A)57.48°
B)57.43°
C)57.38°
D)57.42°

Question 49

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
cos((2n + 1)· 90°)

A)1
B)Undefined
C)0
D)-1

Question 50

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.

Question 51

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.

Question 52

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
(12, 16); Find sin ϴ.

Question 53

Evaluate the expression.

Question 54

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
Lines m and n are parallel.

Question 55

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.

Question 56

Use the properties of angle measures to find the measure of each marked angle.

Question 57

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.

Question 58

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.

Question 59

The triangles are similar. Find the missing side, angle or value of the variable.
50°

Question 60

18
Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .

Question 61

Use the properties of angle measures to find the measure of each marked angle.

Question 62

An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
(-5, -3)

Question 63

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
8 tan 0° + 3 csc 270°

A)3
B)Undefined
C)-3
D)0

Question 64

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.

Question 65

The triangles are similar. Find the missing side, angle or value of the variable.
(3, 6)

Question 66

Use the fundamental identities to find the value of the trigonometric function.
sin ϴ = 7.37

A)Impossible
B)Possible

Question 67

Solve the problem. Round answers to the nearest tenth if necessary.

Question 68

Use the properties of angle measures to find the measure of each marked angle.
tan ϴ > 0 and sin ϴ < 0

A)Quadrant I
B)Quadrant III
C)Quadrant II
D)Quadrant IV

Question 69

Solve the problem.

Question 70

Two quadrilaterals (four-sided figures)are similar. The lengths of the three longest sides of the first quadrilateral are 24 ft, 16 ft, and 12 ft. The lengths of the two shortest sides of the second
Quadrilateral are 18 ft and 9 ft. Find the unknown lengths of the sides of these two figures.

A)The unknown side in the first quadrilateral is 10 ft. The two unknown sides in the second quadrilateral are 27 ft and 24 ft.
B)The unknown side in the first quadrilateral is 8 ft. The two unknown sides in the second quadrilateral are 36 ft and 12 ft.
C)Not enough information is provided.
D)The unknown side in the first quadrilateral is 6 ft. The two unknown sides in the second quadrilateral are 36 ft and 24 ft.

Question 71

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.

A)Possible
B)Impossible

Question 72

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
sec ϴ = 0.97

A)Possible
B)Impossible

Question 73

An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.

Question 74

Decide whether the statement is possible or impossible for an angle .
-180°

A)-180° + n · 360°
B)-180° - n · 180°
C)-180° + n · 180°
D)-180° + 2n · 360°

Question 75

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
52°17´

A)52.34°
B)52.28°
C)53.28°
D)52.17°

Question 76

Evaluate the expression.
AC

Question 77

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.

Question 78

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.

Question 79

Decide whether the statement is possible or impossible for an angle .
BA

Question 80

Identify the quadrant for the angle satisfying the following conditions.
A surveyor recording data for a new subdivision measured an angle as 11.77°. The next day, a different surveyor measured the same angle as 11°31´. Find the difference between these
Measurements (i)to the nearest minute and (ii)to the nearest hundredth of a degree.

A)(i)15´ (ii)0.25°
B)(i)38´ (ii)0.43°
C)(i)77´ (ii)1.29°
D)(i)46´ (ii)0.46°