Trigonometry Quizzes: Test Your Understanding of Trig Functions

Question 1

Determine the exact values of sine, cosine, and tangent for an angle of π/3 using the unit circle.

Accepted Answer

(√3/2, 1/2, √3)

Answer

(1/2, √3/2, 1/√3)

Answer

(√3/2, √3/2, 1)

Answer

(1/2, 1/2, √2)

Question 2

Find the value of sin(π/4) + cos(π/3).

Accepted Answer

1

Answer

0

Answer

2

Answer

-1

Question 3

Which of the following is the period of the trigonometric function y = sin(x)?

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 4

What is the value of cos(π/3)?

Accepted Answer

1/2

Answer

-1/2

Answer

0

Answer

1

Question 5

What is the inverse function of the cosine function?

Accepted Answer

arccos

Answer

arcsin

Answer

arctan

Answer

arccsc

Question 6

What is the domain of the function y = sec(x)?

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except 0

Answer

All real numbers except multiples of π

Question 7

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

Accepted Answer

2π/3

Answer

π/3

Answer

π

Answer

2π

Question 8

If tan(θ) = √3, what is the value of cos(θ)?

Accepted Answer

√3/2

Answer

1/2

Answer

1/√3

Answer

√3/3

Question 9

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

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cotangent

Question 10

Find the value of sin(π/2).

Accepted Answer

1

Answer

0

Answer

-1

Answer

Undefined

Question 11

Which trigonometric identity transforms the sum of two sines into a product of sines?

Accepted Answer

Sum-to-Product Identity

Answer

Pythagorean Identity

Answer

Double-Angle Identity

Answer

Product-to-Sum Identity

Question 12

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

Accepted Answer

Spelling

Answer

Navigation

Answer

Architecture

Answer

Astronomy

Question 13

Convert 120 degrees to radians.

Accepted Answer

π/3

Answer

π/2

Answer

π

Answer

2π/3

Question 14

Determine the amplitude of the function y = -3cos(2x + π/4).

Accepted Answer

3

Answer

1

Answer

2

Answer

-3

Question 15

Which of the following is the reciprocal identity for sine?

Accepted Answer

sinθ = 1/cosθ

Answer

sinθ = 1/tanθ

Answer

cosθ = 1/sinθ

Answer

tanθ = 1/sinθ

Question 16

Which of the following is the double-angle identity for cosine?

Accepted Answer

cos2θ = 2cos²θ - 1

Answer

cos2θ = 1 - 2sin²θ

Answer

sin2θ = 2sinθcosθ

Answer

tan2θ = 2tanθ/(1 - tan²θ)

Question 17

What is the inverse function of sine (x)?

Accepted Answer

arcsine (x)

Answer

cosine (x)

Answer

tangent (x)

Answer

cotangent (x)

Question 18

Evaluate sin(π/6).

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

√2/2

Question 19

A right triangle has a hypotenuse of length 10 units and an angle of 30 degrees. What is the length of the side opposite the 30-degree angle?

Accepted Answer

5√3

Answer

5

Answer

10

Answer

10√3

Question 20

Determine the inverse function of y = tan(x).

Accepted Answer

y = arctan(x)

Answer

y = cot(x)

Answer

y = sec(x)

Answer

y = csc(x)

Question 21

Identify the amplitude of the function y = 2cos(3x).

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 22

Establish the range of the function y = -sin(x) + 1.

Accepted Answer

-2 to 2

Answer

-1 to 1

Answer

0 to 2

Answer

All real numbers

Question 23

In radians, what is the period of the trigonometric sine function?

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

4π

Question 24

Evaluate sin(π/3):

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 25

For the function y = 2cos(3x), what is the amplitude?

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 26

State the inverse function of the cosine function.

Accepted Answer

arccosine

Answer

arcsine

Answer

arctangent

Answer

arccotangent

Question 27

Define the unit circle.

Accepted Answer

A circle with radius 1, centered at the origin

Answer

A circle with circumference 2π, centered at the origin

Answer

A circle with diameter 2, centered at the origin

Answer

A circle that passes through the points (1, 0) and (-1, 0)

Question 28

Which of the following is an identity for the cosine function?

Accepted Answer

cos² θ + sin² θ = 1

Answer

cos θ = 1 - sin θ

Answer

cos θ = tan θ / cot θ

Answer

cos θ = sec θ - 1

Question 29

Find the value of sin(π/3).

Accepted Answer

√3/2

Answer

1/2

Answer

1/4

Answer

√2/2

Question 30

What is the reciprocal of the tangent function?

Accepted Answer

Cotangent

Answer

Secant

Answer

Cosecant

Answer

Sine

Question 31

What is the period of the cosine function?

Accepted Answer

2π

Answer

π

Answer

4π

Answer

6π

Question 32

Express the area of a right triangle in terms of the lengths of its legs using trigonometric ratios.

Accepted Answer

Area = (1 / 2) * base * height

Answer

Area = base * height

Answer

Area = (1 / 4) * base * height

Question 33

Evaluate sin(π/2).

Accepted Answer

1

Answer

0

Answer

-1

Answer

Undefined

Question 34

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

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 35

What is the inverse function of y = cosx?

Accepted Answer

y = arccos(x)

Answer

y = sin⁻¹(x)

Answer

y = tan⁻¹(x)

Answer

y = sec⁻¹(x)

Question 36

Evaluate tan(π/2).

Accepted Answer

Undefined

Answer

0

Answer

1

Answer

π

Question 37

Find the period of y = 2cos(3x + π/4).

Accepted Answer

π/3

Answer

π/6

Answer

π/2

Answer

π

Question 38

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

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 39

Specify the domain of y = tan(x).

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except multiples of π

Answer

All real numbers except 0

Question 40

Which transformation will shift the graph of y = sin(x) up by 2 units and to the left by π/2 units?

Accepted Answer

y = sin(x - π/2) + 2

Answer

y = sin(x + π/2) + 2

Answer

y = sin(x) + 2 - π/2

Answer

y = sin(x) - π/2 + 2

Question 41

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 42

Which of the following is the inverse function of sin(θ)?

Accepted Answer

arcsin(θ)

Answer

cos(θ)

Answer

tan(θ)

Answer

arccos(θ)

Question 43

What is the domain of the function y = sec(x)?

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except multiples of π

Answer

All real numbers except 0

Question 44

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

Accepted Answer

-1 to 1

Answer

0 to 1

Answer

-1 to 0

Answer

0 to 2π

Question 45

Which of the following is the value of sin(π/2)?

Accepted Answer

1

Answer

0

Answer

√2/2

Answer

-1

Question 46

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

Accepted Answer

2

Answer

1

Answer

π

Answer

π/2

Question 47

What is the amplitude of the function y = 3sin(x - π/4)?

Accepted Answer

3

Answer

1

Answer

π/4

Answer

√3

Question 48

Which graph represents the function y = -2tan(x)?

Accepted Answer

A graph with asymptotes at x = ±π/2

Answer

A vertical line passing through the origin

Answer

A horizontal line passing through the origin

Answer

A graph with a period of π

Question 49

In a right triangle, the cosecant of an angle is defined as which of the following ratios?

Accepted Answer

Opposite side divided by hypotenuse

Answer

Adjacent side divided by angle

Answer

Hypotenuse divided by opposite side

Answer

Opposite side divided by adjacent side

Question 50

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

Accepted Answer

0.8

Answer

0.5

Answer

0.2

Answer

0.4

Question 51

Convert the angle measure π/3 radians to degrees.

Accepted Answer

30°

Answer

45°

Answer

60°

Answer

90°

Question 52

Find the value of cos(60°).

Accepted Answer

√3/2

Answer

1/2

Answer

-1/2

Answer

-√3/2

Question 53

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

Accepted Answer

[-1, 1]

Answer

[0, 1]

Answer

[-π/2, π/2]

Answer

[π/4, 3π/4]

Question 54

Which of the following is the inverse function of tangent?

Accepted Answer

arctangent

Answer

arcsine

Answer

arccosine

Answer

arcsecant

Question 55

What is the value of sin(π/6)?

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

√2/2

Question 56

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

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

1

Question 57

What is the sum of the measures of the angles in a quadrilateral?

Accepted Answer

360°

Answer

180°

Answer

540°

Answer

720°

Question 58

What is the inverse of the function y = tan(x)?

Accepted Answer

y = arctan(x)

Answer

y = sec(x)

Answer

y = cos(x)

Answer

y = cot(x)

Question 59

Which trigonometric ratio is equal to the adjacent side divided by the hypotenuse?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 60

Determine the amplitude of the function y = 3sin(2x).

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 61

What is the inverse function of cosine?

Accepted Answer

arcsine

Answer

sine

Answer

cosine

Answer

tangent

Question 62

Which identity is used to find the sum of two cosines?

Accepted Answer

cos(a + b) = cos(a)cos(b) + sin(a)sin(b)

Answer

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Answer

cos(a + b) = sin(a)cos(b) + cos(a)sin(b)

Answer

cos(a + b) = sin(a)cos(b) - cos(a)sin(b)

Question 63

Which trigonometric identity relates sine and cosine?

Accepted Answer

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

Answer

sin(x) + cos(x) = 1

Answer

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

Answer

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

Question 64

Which of the following is the double angle formula for cosine?

Accepted Answer

cos(2θ) = 2cos²(θ) - 1

Answer

cos(2θ) = cos²(θ) - 1

Answer

cos(2θ) = 1 - 2sin²(θ)

Answer

cos(2θ) = 2sin²(θ) - 1