Trigonometry Quizzes: Test Your Understanding of Trig Functions

Question 1

In a right-angled triangle with a hypotenuse of 10 cm and an opposite side of 6 cm, determine the value of the sine of the angle opposite the 6 cm side.

Accepted Answer

0.6

Answer

1

Answer

0.4

Answer

0.8

Question 2

Provide an example of a real-world application of trigonometry.

Accepted Answer

Determining the height of a building using angle of elevation

Answer

Balancing a checkbook

Answer

Writing a poem

Question 3

According to the Pythagorean Theorem, in a right-angled triangle, which side's square is equal to the sum of the squares of the other two sides?

Accepted Answer

Hypotenuse

Answer

Opposite side

Answer

Adjacent side

Question 4

Which trigonometric function is the reciprocal of the sine function?

Accepted Answer

Cosecant

Answer

Secant

Answer

Cosine

Answer

Tangent

Question 5

In the second quadrant of a unit circle, what is the sign of the cosine function?

Accepted Answer

Negative

Answer

Undefined

Answer

Positive

Answer

Zero

Question 6

Which trigonometric identity is universally true for all angles?

Accepted Answer

sin²θ + cos²θ = 1

Answer

cscθ = 1 / sinθ

Answer

cotθ = cosθ / sinθ

Answer

tanθ = sinθ / cosθ

Question 7

What is the period of the sine function?

Accepted Answer

2π

Answer

4π

Answer

π

Answer

8π

Question 8

Which of the following definitions correctly describes the sine function?

Accepted Answer

The ratio of the length of the opposite side to the length of the hypotenuse of a right triangle

Answer

The ratio of the length of the hypotenuse to the length of the opposite side

Answer

The ratio of the length of the adjacent side to the length of the hypotenuse

Question 9

Which of the following scenarios best exemplifies an application of the tangent function?

Accepted Answer

Determining the height of a tall building

Answer

Calculating the distance to a star

Answer

Estimating the volume of a sphere

Answer

Finding the area of a circle

Question 10

Which trigonometric identity holds true for all angles θ?

Accepted Answer

sin²θ + cos²θ = 1

Answer

secθ = tanθ/sinθ

Answer

cotθ = 1/tanθ

Answer

cscθ = sinθ/cosθ

Question 11

What is the period of the sine function?

Accepted Answer

2π

Answer

3π/2

Answer

4π

Answer

π

Question 12

Identify the graph that accurately represents the function y = -cos(x).

Accepted Answer

Image of a cosine graph reflected over the x-axis

Answer

Image of a cosine graph translated 2 units to the left

Answer

Image of a cosine graph shifted 1 unit up

Answer

Image of a cosine graph stretched vertically by a factor of 3

Question 13

Which of the following correctly defines the sine function?

Accepted Answer

The ratio of the length of the side opposite the angle to the length of the hypotenuse

Answer

The ratio of the length of the adjacent side to the length of the opposite side

Answer

The ratio of the length of the adjacent side to the length of the hypotenuse

Question 14

Which of the following trigonometric identities is the defining identity for the cosine function?

Accepted Answer

cos²(θ) + sin²(θ) = 1

Answer

cos(θ) - sin(θ) = 1

Answer

sin²(θ) - cos²(θ) = 1

Answer

cos(θ) + sin(θ) = 1

Question 15

What is the period of the sine function?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 16

Identify an example of a practical application of trigonometry.

Accepted Answer

Employing trigonometric principles to determine the height of a structure based on the angle of elevation

Answer

Solving equations that are quadratic in nature

Answer

Calculating the area of a circular region

Question 17

What is the radian equivalent of an angle measuring 120°?

Accepted Answer

2π/3

Answer

π/3

Answer

3π/2

Answer

π/6

Question 18

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

Accepted Answer

2

Answer

1

Answer

π

Answer

-2

Question 19

Describe the domain of the function y = tan(x).

Accepted Answer

All real numbers except for those that are multiples of π/2

Answer

All real numbers

Answer

All real numbers between -π/2 and π/2

Answer

All positive real numbers

Question 20

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

Accepted Answer

Sine

Answer

Tangent

Answer

Cosine

Question 21

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

Accepted Answer

Cosine

Answer

Sine

Answer

Cotangent

Answer

Tangent

Question 22

What is the value of cos(0°)?

Accepted Answer

1

Answer

0.5

Answer

-1

Answer

0

Question 23

Which of the following is the inverse function of sine?

Accepted Answer

arcsin

Answer

tan

Answer

cos

Answer

csc

Question 24

Which of the following is NOT a trigonometric function?

Accepted Answer

Exponential

Answer

Tangent

Answer

Cosine

Answer

Sine

Question 25

In a right triangle with a hypotenuse of length 20 and an angle of 30 degrees, what is the length of the side opposite the angle?

Accepted Answer

10

Answer

20

Answer

5

Answer

15

Question 26

Which of the following is the period of the sine function?

Accepted Answer

2π

Answer

3π

Answer

1

Answer

π

Question 27

Which of the following is the range of the sine function?

Accepted Answer

[-1, 1]

Answer

The real numbers

Answer

The positive real numbers

Answer

The integers

Question 28

Which of the following is the definition of the sine function in a right triangle?

Accepted Answer

The ratio of the length of the opposite side to the length of the hypotenuse

Answer

The ratio of the length of the adjacent side to the length of the hypotenuse

Answer

The ratio of the length of the hypotenuse to the length of the opposite side

Answer

The ratio of the length of the adjacent side to the length of the opposite side

Question 29

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

Accepted Answer

A periodic curve that oscillates between -1 and 1

Answer

A circle

Answer

A parabola

Answer

A straight line

Question 30

Which of the following is the equation of a unit circle?

Accepted Answer

x² + y² = 1

Answer

x² - y² = 1

Answer

y² - x² = 1

Answer

x + y = 1

Question 31

In a right triangle, the angle opposite the side of length x is 30 degrees, and the hypotenuse is 10 units long. What is the length of side x?

Accepted Answer

5 units

Answer

10 units

Answer

7.5 units

Answer

2.5 units

Question 32

Find the value of tan(60°) :

Accepted Answer

√3

Answer

1

Answer

1/2

Answer

2

Question 33

A ladder with a length of 10 meters is leaning against a wall. If the foot of the ladder is 6 meters away from the wall, calculate the angle (to the nearest degree) the ladder makes with the ground:

Accepted Answer

53°

Answer

75°

Answer

45°

Answer

60°

Question 34

Determine the period of the function y = sin(2x):

Accepted Answer

π

Answer

π/2

Answer

4π

Answer

2π

Question 35

Which of the following angles is NOT a quadrantal angle?

Accepted Answer

60°

Answer

0°

Answer

180°

Answer

90°

Question 36

Find the amplitude of the function y = 3sin(x):

Accepted Answer

3

Answer

π

Answer

2π

Answer

1

Question 37

A Ferris wheel with a 60-meter diameter completes one full rotation in 5 minutes. Calculate the speed (in meters per second) of a rider on the Ferris wheel:

Accepted Answer

0.628 m/s (approximately)

Answer

1.256 m/s (approximately)

Answer

3.14 m/s (approximately)