Trigonometry Quizzes: Test Your Understanding of Angles and Triangles

Question 1

Which equation represents the trigonometric identity known as the Pythagorean identity?

Accepted Answer

sin²x + cos²x = 1

Answer

sin²x - cos²x = 0

Answer

sin²x > cos²x

Answer

sin²x = cos²x

Question 2

In a right triangle, what is the definition of the sine of an angle?

Accepted Answer

Opposite side divided by hypotenuse

Answer

Adjacent side divided by opposite side

Answer

Hypotenuse divided by adjacent side

Answer

Opposite side divided by adjacent side

Question 3

In a right triangle, what is the ratio of the length of the opposite side to the length of the hypotenuse called?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Question 4

Which formula defines the sine ratio in a right triangle?

Accepted Answer

sin(theta) = opposite / hypotenuse

Answer

cos(theta) = adjacent / hypotenuse

Answer

tan(theta) = opposite / adjacent

Answer

cot(theta) = adjacent / opposite

Question 5

In a right triangle, what is the sine of an angle measuring 30 degrees?

Accepted Answer

0.5

Answer

0.75

Answer

1

Answer

2

Question 6

In which quadrant does the terminal side of an angle with a sine value of -0.5 lie?

Accepted Answer

III

Answer

II

Question 7

Find the value of cos(π/3):

Accepted Answer

√3/2

Answer

0

Answer

1/2

Question 8

A Ferris wheel has a diameter of 50 meters. If a passenger boards 10 meters above the ground, what is the height of the passenger at the highest point of the wheel?

Accepted Answer

30 m

Answer

10 m

Question 9

Which of the following is the inverse function of cosine?

Accepted Answer

Arccosine

Answer

Cosine

Question 10

Which trigonometric function is used to find the length of the side adjacent to the angle of interest in a right triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 11

Which of the following is NOT a trigonometric function?

Accepted Answer

Exponential

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 12

If the length of the hypotenuse in a right triangle is 13 and the length of the adjacent side is 5, what is the length of the opposite side?

Accepted Answer

10

Answer

8

Answer

12

Answer

15

Question 13

Which quadrant does the terminal side of an angle of 225° lie in?

Accepted Answer

III

Answer

I

Answer

II

Answer

IV

Question 14

In a right triangle with a 30-degree angle and a hypotenuse of 10 cm, what is the length of the opposite side?

Accepted Answer

5√3 cm

Answer

5 cm

Answer

2√3 cm

Answer

10 cm

Question 15

Which of the following is not a trigonometric function?

Accepted Answer

Quadratic

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 16

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 17

Which of the following is the graph of the cosine function?

Accepted Answer

A wave

Answer

A straight line

Answer

A parabola

Answer

A circle

Question 18

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

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 19

The graph of the function y = sin(x) has a period of:

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 20

In a navigation problem, a ship sails 100 miles due north and then 50 miles due east. What is the distance between the starting point and the final destination?

Accepted Answer

112 miles

Answer

50 miles

Answer

100 miles

Answer

150 miles

Question 21

Which of the following identities is true for all angles θ?

Accepted Answer

sin²(θ) + cos²(θ) = 1

Answer

tan(θ) = sin(θ) / cos(θ)

Answer

cot(θ) = cos(θ) / sin(θ)

Answer

sec(θ) = sin(θ) / cos(θ)

Question 22

If the tangent of an angle is 0.5, what is the measure of the angle (in degrees)?

Accepted Answer

26.57°

Answer

30°

Answer

45°

Answer

60°

Question 23

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

Accepted Answer

2

Answer

1

Answer

π

Answer

2π

Question 24

What is the vertical translation of the function y = cos(x) - 2?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 25

Which trigonometric function is used to find the length of the side adjacent to an angle in a right triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cotangent

Question 26

Which of the following is NOT a unit of angle measure?

Accepted Answer

Millimeters

Answer

Degrees

Answer

Radians

Answer

Gradians

Question 27

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

Accepted Answer

opposite side over hypotenuse

Answer

adjacent side over hypotenuse

Answer

hypotenuse over opposite side

Answer

opposite side over adjacent side

Question 28

Given a right triangle with legs of length 3 and 4, find the length of the hypotenuse.

Accepted Answer

7

Answer

5

Answer

12

Answer

5/3

Question 29

Which of the following is not a trigonometric function?

Accepted Answer

base-10 logarithm

Answer

sine

Answer

cosine

Answer

tangent

Question 30

Find the period of the function y = sin(2x).

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

π/4

Question 31

Identify the graph of y = 2cos(x).

Accepted Answer

Cosine curve with amplitude 2

Answer

Cosine curve with amplitude 1

Answer

Sine curve with amplitude 1

Answer

Sine curve with amplitude 2

Question 32

What is the inverse function of the sine function?

Accepted Answer

arcsine

Answer

cosine

Answer

tangent

Answer

cotangent

Question 33

If the measure of one acute angle in a right triangle is 30 degrees, then the measure of its complement is:

Accepted Answer

60 degrees

Answer

15 degrees

Answer

30 degrees

Answer

90 degrees

Question 34

Which of the following is NOT a trigonometric function?

Accepted Answer

Quadratic

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 35

The inverse of the cosine function is:

Accepted Answer

Arccosine

Answer

Arcsine

Answer

Arctangent

Answer

Arccotangent

Question 36

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

Accepted Answer

45 degrees

Answer

30 degrees

Answer

60 degrees

Answer

90 degrees

Question 37

In a right triangle, what is the tangent of a 30-degree angle?

Accepted Answer

1/2

Answer

1

Answer

2

Answer

0

Question 38

In a right triangle, which trigonometric ratio represents the ratio of the length of the side opposite an angle to the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Question 39

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

Accepted Answer

Opposite side

Answer

Adjacent side

Answer

Angle

Question 40

In a right triangle with a 30-degree angle, what is the sine's value?

Accepted Answer

1/2

Answer

1/4

Answer

2/3

Answer

1

Question 41

Identify the Pythagorean Identity:

Accepted Answer

sin^2(x) + cos^2(x) = 1

Answer

tan(x) = sin(x) / cos(x)

Answer

cos(x) / sin(x) = cot(x)

Answer

sin(x) + cos(x) = 1

Question 42

Which function represents the inverse of cosine?

Accepted Answer

arccos(x)

Answer

arcsin(x)

Answer

arctan(x)

Answer

arccot(x)

Question 43

Write the equation for the graph of a cosine function with an amplitude of 3 and a period of 2π.

Accepted Answer

y = 3cos(x)

Answer

y = 3sin(x)

Answer

y = cos(3x)

Answer

y = sin(2πx)

Question 44

Which method is NOT used to solve right triangles?

Accepted Answer

Heron's Formula

Answer

Pythagorean Theorem

Answer

Law of Sines

Answer

Law of Cosines

Question 45

Which of the following is not a trigonometric function?

Accepted Answer

Quadratic

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 46

What is the value of cos(90 degrees)?

Accepted Answer

0

Answer

1

Answer

undefined

Answer

π/2

Question 47

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 ground?

Accepted Answer

45 degrees

Answer

30 degrees

Answer

60 degrees

Answer

75 degrees

Question 48

Which of the following is the Pythagorean identity?

Accepted Answer

sin² θ + cos² θ = 1

Answer

tan² θ = 1 + cot² θ

Answer

csc² θ - sec² θ = 1

Answer

sin θ + cos θ = 1

Question 49

What is the period of the sine or cosine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 50

Which of the following graphs represents the function y = 2sin(x)?

Accepted Answer

A graph of a sine wave with amplitude 2

Answer

A graph of a cosine wave with amplitude 2

Answer

A graph of a parabola with vertex (0,2)

Answer

A graph of a straight line with slope 2

Question 51

Which of the following is a unit circle?

Accepted Answer

A circle with radius 1

Answer

A circle with radius π

Answer

A circle with radius 2π

Answer

A circle with radius 1/2

Question 52

What is the inverse function of sine?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Arccosine

Question 53

In a right triangle, which trigonometric ratio is calculated by dividing the length of the opposite side by the length of the hypotenuse?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 54

In a right triangle, the ratio of the length of the side opposite a given angle to the length of the hypotenuse is called the what?

Accepted Answer

Sine ratio

Answer

Cosine ratio

Answer

Tangent ratio

Question 55

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

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Secant

Question 56

Which trigonometric function represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 57

In a right triangle with an angle of 30 degrees and a hypotenuse of 10 inches, what is the length of the opposite side?

Accepted Answer

5 inches

Answer

8.66 inches

Answer

10 inches

Answer

17.32 inches

Question 58

Which of the following is NOT a valid application of trigonometry in the real world?

Accepted Answer

Counting money

Answer

Navigation

Answer

Engineering

Answer

Medicine

Question 59

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to:

Accepted Answer

The sum of the squares of the lengths of the other two sides

Answer

The difference of the squares of the lengths of the other two sides

Answer

The product of the lengths of the other two sides

Answer

The quotient of the lengths of the other two sides

Question 60

If the length of the hypotenuse of a right triangle is 10 cm and the length of one of the other sides is 6 cm, what is the length of the remaining side?

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

10 cm

Question 61

A ship sails 100 miles due east and then turns and sails 50 miles due north. Using trigonometry, how far is the ship from its starting point?

Accepted Answer

112 miles

Answer

50 miles

Answer

100 miles

Answer

150 miles

Question 62

Which of the following is the Pythagorean theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

c^2 - a^2 = b^2

Answer

(a + b)^2 = c^2

Question 63

In a right triangle with one angle measuring 45 degrees, what is the length of the hypotenuse if one leg is 5 inches?

Accepted Answer

7.07 inches

Answer

5 inches

Answer

10 inches

Question 64

Which trigonometric identity relates the sine and cosine functions?

Accepted Answer

sin^2(x) + cos^2(x) = 1

Answer

tan^2(x) + cos^2(x) = 1

Answer

sin^2(x) - cos^2(x) = 1