Trigonometry Quizzes: Master Trig Functions and Identities

Question 1

Calculate the sine of a 30-degree angle.

Accepted Answer

√3/2

Answer

1/2

Answer

1

Answer

√2/2

Question 2

Which trigonometric identity establishes the relationship between sine and cosine functions?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tanθ = sinθ / cosθ

Answer

sin(θ + π) = -sinθ

Answer

cos(θ - π/2) = sinθ

Question 3

Identify the equation that represents the graph of a cosine function with an amplitude of 3 and a period of 2π.

Accepted Answer

y = 3cos(x)

Answer

y = 3cos(2x)

Answer

y = cos(3x)

Answer

y = 3cos(x/2)

Question 4

Specify the domain of the sine function.

Accepted Answer

All real numbers

Answer

[-1, 1]

Answer

[0, 2π]

Answer

[-π, π]

Question 5

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

Accepted Answer

2

Answer

1

Answer

3

Answer

π/2

Question 6

Which trigonometric identity is utilized to establish the Pythagorean identity?

Accepted Answer

sin²θ + cos²θ = 1

Answer

tanθ = sinθ / cosθ

Answer

sin(θ + π) = -sinθ

Answer

cos(θ - π/2) = sinθ

Question 7

What is the sine of 90 degrees?

Accepted Answer

1

Answer

0

Answer

2

Answer

-1

Question 8

What is the period of the trigonometric function y = cos x?

Accepted Answer

2π

Answer

π

Answer

4π

Answer

6π

Question 9

What is the inverse trigonometric function of y = sin x?

Accepted Answer

sin⁻¹ x

Answer

cos⁻¹ x

Answer

tan⁻¹ x

Answer

sec⁻¹ x

Question 10

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

Accepted Answer

Length of the opposite side divided by the length of the hypotenuse

Answer

Length of the adjacent side divided by the length of the opposite side

Answer

Length of the hypotenuse divided by the length of the opposite side

Answer

Length of the opposite side divided by the length of the adjacent side

Question 11

Which trigonometric identity is used as a fundamental tool to verify other trigonometric identities?

Accepted Answer

Pythagorean Identity

Answer

Sum and Difference Identities

Answer

Double Angle Identities

Answer

Half Angle Identities

Question 12

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

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

4π

Question 13

Which of the following is the amplitude of the function y = 2cos(3x)?

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 14

Which of the following equations represents a cosine function with a phase shift of π/3 radians to the right?

Accepted Answer

y = cos(x + π/3)

Answer

y = cos(x - π/3)

Answer

y = -cos(x - π/3)

Answer

y = -cos(x + π/3)

Question 15

What is the maximum value of the function y = 3sin(x - π/2)?

Accepted Answer

3

Answer

1

Answer

6

Answer

9

Question 16

In trigonometry, which ratio represents the adjacent side divided by the hypotenuse?

Accepted Answer

Cosine

Answer

Sine

Answer

Tangent

Answer

Cosecant

Question 17

What is the period of the sine function?

Accepted Answer

$2pi$

Answer

$pi/2$

Answer

$pi$

Answer

$4pi$

Question 18

Which function is the inverse of the sine function?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 19

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

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

4π

Question 20

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

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 21

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

Accepted Answer

A cosine wave

Answer

A line with a positive slope

Answer

A line with a negative slope

Answer

A parabola opening upward

Question 22

Which of the following is a unit circle?

Accepted Answer

A circle with a radius of 1

Answer

A circle with a diameter of 2

Answer

A circle that is inscribed in a square

Answer

A circle that is circumscribed about a square

Question 23

Which trigonometric ratio is determined by the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 24

Which trigonometric identity relates the sine, cosine, and tangent of the same angle?

Accepted Answer

Pythagorean Identity (sin²x + cos²x = 1)

Answer

Double Angle Identity (sin(2x) = 2sin(x)cos(x))

Answer

Half Angle Identity (sin(x/2) = ±√((1 - cos(x))/2))

Answer

Sum and Difference Identities (sin(x ± y) = sin(x)cos(y) ± cos(x)sin(y))

Question 25

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

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 26

Which function is the inverse of the cosine function?

Accepted Answer

Arccosine

Answer

Sine

Answer

Arcsine

Answer

Cosine

Question 27

What is the range of the tangent function?

Accepted Answer

(-∞, ∞)

Answer

[-1, 1]

Answer

(0, ∞)

Answer

(-∞, 0)

Question 28

Identify the graph that represents y = sin θ.

Accepted Answer

A sine wave

Answer

A straight line

Answer

A circle

Answer

A parabola

Question 29

Find the amplitude of the function y = 2 sin θ.

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 30

Identify the inverse function of sine.

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 31

Which trigonometric ratio relates the opposite side to the hypotenuse of a right triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cosecant

Question 32

Which trigonometric identity is used to find sin(2x) in terms of sin(x) and cos(x)?

Accepted Answer

sin(2x) = 2sin(x)cos(x)

Answer

sin(2x) = sin(x)cos(x)

Answer

sin(2x) = 2cos(x)sin(x)

Answer

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

Question 33

What is the period of the function f(x) = 3cos(2πx)?

Accepted Answer

2

Answer

1

Answer

π/2

Answer

π

Question 34

Which function is the inverse of the cosine function?

Accepted Answer

Arccosine

Answer

Sine

Answer

Cosine

Answer

Arcsine

Question 35

Which of the following is equivalent to an angle of 150 degrees in radians?

Accepted Answer

5π/6

Answer

π/6

Answer

π/3

Answer

π

Question 36

What is the value of cos(π)?

Accepted Answer

-1

Answer

0

Answer

1

Answer

Undefined

Question 37

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

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 38

Find the value of tan(π/4).

Accepted Answer

√2

Answer

1

Answer

2

Answer

√3

Question 39

Find 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 40

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

Accepted Answer

3

Answer

-3

Answer

1

Answer

-1

Question 41

Which of the following trigonometric identities relates sine, cosine, and tangent?

Accepted Answer

sin²x + cos²x = 1

Answer

tan²x + cot²x = 1

Answer

sin(x+y) = sinxcosy + cosxsin

Answer

cos(x-y) = cosxcosy + sinxsiny

Question 42

Which angle has a sine value of 1/2?

Accepted Answer

30°

Answer

60°

Answer

90°

Answer

45°

Question 43

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

Accepted Answer

2

Answer

4

Answer

-2

Answer

1

Question 44

Which of the following is a real-world application of trigonometry?

Accepted Answer

Navigation

Answer

Algebra

Answer

Calculus

Answer

Biology

Question 45

In a right triangle ABC with angle A = 90°, what is the value of cos(B)?

Accepted Answer

adjacent side / hypotenuse

Answer

hypotenuse / adjacent side

Answer

adjacent side / opposite side

Answer

opposite side / hypotenuse

Question 46

In a right triangle, the sine of an angle is defined as which of these ratios?

Accepted Answer

Opposite side length / Hypotenuse length

Answer

Adjacent side length / Hypotenuse length

Answer

Hypotenuse length / Opposite side length

Question 47

The Pythagorean identity for sine and cosine is:

Accepted Answer

sin² θ + cos² θ = 1

Answer

cos² θ + sin² θ = 0

Answer

cos² θ - sin² θ = 1

Answer

sin² θ - cos² θ = 1

Question 48

Find the value of sin 30°:

Accepted Answer

1/2

Answer

0

Answer

1

Answer

√3/2

Question 49

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

Accepted Answer

2π

Answer

4π

Answer

π/2

Answer

π

Question 50

Find the amplitude of the function y = 2cos(3x + π/4):

Accepted Answer

2

Answer

1

Answer

3

Question 51

Solve for θ in the equation 2cos θ - 1 = 0:

Accepted Answer

θ = π/3, 5π/3

Answer

θ = π/2, 3π/2

Answer

θ = π/4, 3π/4

Answer

θ = π/6, 5π/6

Question 52

Find the value of tan(π/4):

Accepted Answer

1

Answer

√3/2

Answer

0

Answer

√2/2

Question 53

Which of the following graphs represents the function y = -cos x?

Accepted Answer

The cosine graph flipped vertically about the x-axis

Answer

The cosine graph flipped vertically about the y-axis

Answer

The cosine graph flipped horizontally about the x-axis

Question 54

Find the domain of the function y = tan x:

Accepted Answer

All real numbers except odd multiples of π/2

Answer

All real numbers except multiples of π

Answer

All real numbers between -π and π

Answer

All real numbers