Trigonometry Quizzes: Master Trig Ratios and Solve Right Triangles

Question 1

In a right-angled triangle, what is the sine function defined as?

Accepted Answer

Opposite side divided by the hypotenuse

Answer

Adjacent side divided by the hypotenuse

Answer

Opposite side divided by the adjacent side

Answer

Hypotenuse divided by the adjacent side

Question 2

Which function is the inverse of the cosine function?

Accepted Answer

Arccosine

Answer

Sine

Answer

Cosine

Answer

Arcsine

Question 3

What is the period of the sine function?

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

3π

Question 4

Which identity is the reciprocal identity for the cosine function?

Accepted Answer

cos(x) = 1/sin(x)

Answer

sin(x) = 1/cos(x)

Answer

tan(x) = 1/cos(x)

Answer

cot(x) = 1/sin(x)

Question 5

Which of the following is the inverse trigonometric function of cosine?

Accepted Answer

Arccosine

Answer

Sine

Answer

Tangent

Question 6

In a right triangle, the ratio of the opposite side to the hypotenuse is equal to the:

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Question 7

In a right triangle, the side that is directly across from the angle of interest is called the:

Accepted Answer

Opposite

Answer

Hypotenuse

Answer

Adjacent

Answer

Sine

Question 8

What is the value of sin(30°)?

Accepted Answer

0.5

Answer

0.75

Answer

1

Answer

1.5

Question 9

What is the value of cos(π/4)?

Accepted Answer

√2/2

Answer

0

Answer

1/2

Answer

1

Question 10

Which of the following trigonometric identities is true?

Accepted Answer

sin²x + cos²x = 1

Answer

tanx = sinx / cosx

Answer

cscx = cosx / sinx

Answer

cotx = sinx / tanx

Question 11

In a right triangle, which ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Secant

Question 12

What is the period of the function y = 2sin(3x)?

Accepted Answer

2pi/3

Answer

pi/3

Answer

pi/6

Answer

2pi/6

Question 13

Which of the following is true about the graph of the function y = tan(x)?

Accepted Answer

It has vertical asymptotes at x = pi/2 and x = 3pi/2.

Answer

It has vertical asymptotes at x = 0 and x = pi.

Answer

It has no vertical asymptotes.

Answer

It has horizontal asymptotes at y = 1 and y = -1.

Question 14

A ladder leans against a wall, forming an angle of 60 degrees with the ground. If the base of the ladder is 8 feet from the wall, what is the length of the ladder?

Accepted Answer

13.86 feet

Answer

8 feet

Answer

16 feet

Answer

6.93 feet

Question 15

Evaluate the expression cos(π/6) - sin(π/3):

Accepted Answer

-0.5

Answer

0

Answer

0.5

Answer

1

Question 16

Which of the following is the graph of the function y = 2sin(x)?

Accepted Answer

A sine curve with an amplitude of 2

Answer

A cosine curve with an amplitude of 2

Answer

A sine curve with an amplitude of 1

Answer

A cosine curve with an amplitude of 1

Question 17

In a right triangle, which ratio represents the relationship between the opposite side and the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 18

Which of the following is the inverse trigonometric function of sine?

Accepted Answer

Arcsine

Answer

Arccosine

Answer

Arctangent

Answer

Arccotangent

Question 19

What is the amplitude of the function y = 2sin(3x + π/2)?

Accepted Answer

2

Answer

1

Answer

3

Answer

π/2

Question 20

A ship sails 40 miles on a course of 15 degrees south of west. How far south and how far west has the ship traveled?

Accepted Answer

33.1 miles south, 26.9 miles west

Answer

26.9 miles south, 33.1 miles west

Answer

15 miles south, 40 miles west

Question 21

In a right triangle, the tangent of an angle is the ratio of which two sides?

Accepted Answer

Opposite and adjacent

Answer

Adjacent and opposite

Answer

Hypotenuse and opposite

Answer

Hypotenuse and adjacent

Question 22

In trigonometry, what is the definition of amplitude? Provide an example to illustrate your answer.

Accepted Answer

Amplitude is the vertical distance from the midline of the function to its maximum or minimum value.

Answer

Amplitude is the number of cycles completed in a given time period.

Answer

Amplitude is the horizontal shift of the trigonometric function.

Answer

Amplitude is the measure of how quickly the function oscillates.

Question 23

Analyze the sine and cosine functions. How do they differ in terms of symmetry, range, and number of extrema?

Accepted Answer

The sine function is odd and has a range of [-1, 1], while the cosine function is even and has the same range.

Answer

The sine and cosine functions have different periods but the same range and number of extrema.

Answer

The sine function has a vertical shift of 1 unit, while the cosine function has no vertical shift.

Answer

The sine and cosine functions have the same symmetry but different periods.

Question 24

Which trigonometric ratio is used to find the length of the side adjacent to the known angle?

Accepted Answer

Cosine

Answer

Secant

Answer

Tangent

Answer

Sine

Question 25

In a right triangle with an angle of 30 degrees and a hypotenuse of 10 cm, find the length of the opposite side.

Accepted Answer

5 cm

Answer

20 cm

Answer

10 cm

Answer

15 cm

Question 26

Which of the following is the inverse function of cosine?

Accepted Answer

Arccosine

Answer

Sine

Answer

Secant

Answer

Tangent

Question 27

Which of the following identities is true?

Accepted Answer

sin²x + cos²x = 1

Answer

sec²x - cos²x = 1

Answer

tan²x + cot²x = 1

Answer

sin²x - cos²x = 1

Question 28

In a circle with radius r, the length of the arc intercepted by a central angle of θ radians is given by:

Accepted Answer

rθ

Answer

r²/θ

Answer

θr²

Answer

θ²/r

Question 29

In a right triangle, the cosine of an angle is defined as the ratio of which two sides?

Accepted Answer

adjacent side to hypotenuse

Answer

hypotenuse to opposite side

Answer

opposite side to adjacent side

Answer

opposite side to hypotenuse

Question 30

The tangent of an angle in a right triangle is defined as which of the following ratios?

Accepted Answer

opposite side divided by adjacent side

Answer

adjacent side divided by opposite side

Answer

hypotenuse divided by opposite side

Answer

hypotenuse divided by adjacent side

Question 31

Which of the following expressions is equivalent to sin(90°)?

Accepted Answer

1

Answer

π/2

Answer

-1

Answer

0

Question 32

If the sine of an angle is 0.6, what is the cosine of its complementary angle?

Accepted Answer

0.8

Answer

0.4

Answer

0.6

Answer

Cannot be determined

Question 33

In a right triangle, the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle is known as the:

Accepted Answer

Sine

Answer

Cosine

Answer

Cotangent

Answer

Tangent

Question 34

A ladder is leaning against a wall. The base of the ladder is 6 feet from the wall, and the top of the ladder is 10 feet high. What is the angle between the ladder and the wall?

Accepted Answer

arctan(10/6) ≈ 60°

Answer

arccot(10/6) ≈ 30°

Answer

arccos(10/6) ≈ 34°

Answer

arcsin(10/6) ≈ 56°

Question 35

Which trigonometric identity is used to find the value of sin²θ + cos²θ?

Accepted Answer

1

Answer

sinθ + cosθ

Answer

sinθ - cosθ

Answer

0

Question 36

Which of the following is the graph of the function y = cos(x - π/2)?

Accepted Answer

Shifted cosine curve to the right by π/2 units

Answer

Stretched cosine curve

Answer

Shifted cosine curve to the left by π/2 units

Question 37

What is the amplitude of the function y = 2cos(3x + π/4)?

Accepted Answer

2

Answer

3

Answer

1

Question 38

Which of the following is a unit circle?

Accepted Answer

A circle with a radius of 1 centered at the origin of the coordinate plane

Answer

A circle with any radius centered at any point

Answer

An ellipse

Question 39

What is the value of sin(π/3)?

Accepted Answer

√3/2

Answer

1/2

Answer

-1/2

Answer

-√3/2

Question 40

Which of the following is a radian measure of a 45° angle?

Accepted Answer

π/4

Answer

π/2

Answer

π/6

Answer

π/3

Question 41

In a right triangle, the sine of an angle is defined as the ratio of:

Accepted Answer

Opposite side / Hypotenuse

Answer

Adjacent side / Opposite side

Answer

Hypotenuse / Adjacent side

Answer

Opposite side / Adjacent side

Question 42

A ladder is leaning against a wall. The ladder is 10 feet long and the base of the ladder is 6 feet from the wall. What is the angle between the ladder and the ground?

Accepted Answer

arctan(6/10)

Answer

tan-1(10/6)

Answer

cos-1(6/10)

Answer

sin-1(6/10)

Question 43

Which of the following is NOT a unit circle angle?

Accepted Answer

120 degrees

Answer

0 degrees

Answer

270 degrees

Answer

90 degrees

Question 44

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

1

Question 45

What is the amplitude of the function y = 2sin(3x)?

Accepted Answer

2

Answer

6

Answer

1

Answer

3

Question 46

What is the inverse function of sine?

Accepted Answer

arcsin

Answer

cos^-1

Answer

cot^-1

Answer

tan^-1

Question 47

Which of the following is a solution to the equation tan(x) = 1?

Accepted Answer

x = π/4 + nπ, where n is an integer

Answer

x = π + nπ, where n is an integer

Answer

x = π/2 + nπ, where n is an integer

Answer

x = 0 + nπ, where n is an integer