Trigonometric Functions: Interactive Learning Quizzes for Tenth Grade Math

Question 1

Which trigonometric identity expresses sin(x - y) in terms of sin x, cos x, sin y, and cos y?

Accepted Answer

sin(x - y) = sin x cos y - cos x sin y

Answer

sin(x - y) = sin x + cos y

Answer

sin(x - y) = cos x cos y - sin x sin y

Answer

sin(x - y) = cos x sin y + sin x cos y

Question 2

What is the value of tan(π/4)?

Accepted Answer

√2

Answer

0

Answer

1

Answer

2

Question 3

Which mathematical operation is NOT a trigonometric function?

Accepted Answer

Exponentiation

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 4

What is the domain of the cosine function?

Accepted Answer

All real numbers

Answer

[-1, 1]

Answer

[-π/2, π/2]

Answer

[-π, π]

Question 5

Which of the following equations represents the graph of y = sin(x) shifted π/2 units to the right?

Accepted Answer

y = sin(x + π/2)

Answer

y = sin(x - π/2)

Answer

y = cos(x)

Answer

y = -sin(x)

Question 6

What is the period of the function y = cos(2x), written in terms of π?

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

2π/3

Question 7

The inverse function of y = tan(x) is:

Accepted Answer

y = arctan(x)

Answer

y = cot(x)

Answer

y = sec(x)

Answer

y = csc(x)

Question 8

Which of the following is the inverse function of sine?

Accepted Answer

Arcsine

Answer

Cosine

Answer

Tangent

Answer

Arccosine

Question 9

Which of these graphs depicts the function y = sin(x)?

Accepted Answer

A sinusoidal curve that ranges from -1 to 1, with a maximum value of 1 and a minimum value of -1.

Answer

A straight line with a slope of 1.

Answer

A parabola that opens upwards.

Answer

A parabola that opens downwards.

Question 10

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 11

Which practical application of trigonometry is used in the field of navigation?

Accepted Answer

Finding the direction of a ship

Answer

Calculating the height of a building

Answer

Determining the distance to a star

Answer

Measuring the speed of a car

Question 12

Which graph accurately depicts the function y = sin(x)?

Accepted Answer

A wave oscillating between -1 and 1, crossing the x-axis at multiples of π

Answer

A straight line with a positive slope

Answer

A circle passing through (-1, 0), (0, 1), and (1, 0)

Answer

A parabola opening downward with its vertex at (0, 1)

Question 13

Which of the following identities is true?

Accepted Answer

sin²x + cos²x = 1

Answer

sin(x + y) = sinx + siny

Answer

cos(x - y) = cosx + cosy

Answer

tanx = sinx/cosx

Question 14

What is the inverse function of the cosine function?

Accepted Answer

arcos(x)

Answer

arcsin(x)

Answer

arctan(x)

Answer

sec(x)

Question 15

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

Accepted Answer

cos(x)

Answer

-sin(x)

Answer

-cos(x)

Answer

sin(x)

Question 16

What is the range of the tangent function?

Accepted Answer

(-∞, ∞)

Answer

[-1, 1]

Answer

[-π/2, π/2]

Answer

[0, ∞)

Question 17

Which trigonometric identity is true for all angles θ?

Accepted Answer

sin²(θ) + cos²(θ) = 1

Answer

sin(θ) + cos(θ) = 0

Answer

sin(θ) - cos(θ) = 1

Answer

tan(θ) = sin(θ) / cos(θ)

Question 18

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

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 19

Which equation represents a vertical translation of the sine function by 2 units?

Accepted Answer

y = sin(x) + 2

Answer

y = sin(x - 2)

Answer

y = 2sin(x)

Answer

y = sin(2x)

Question 20

Solve the equation sin(x) = 0.5 for 0 ≤ x ≤ 2π:

Accepted Answer

x = π/6, 5π/6

Answer

x = π/3, 2π/3

Answer

x = π/4, 3π/4

Answer

x = 0, π

Question 21

What is the inverse function of the cosine function?

Accepted Answer

Arccosine function

Answer

Sine function

Answer

Tangent function

Answer

Arcsine function

Question 22

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

Accepted Answer

π/3

Answer

π

Answer

2π

Answer

3π

Question 23

What is the value of sin(π/3) - cos(π/4)?

Accepted Answer

√3/2

Answer

0

Answer

1

Answer

√2/2

Question 24

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

Accepted Answer

2π

Answer

1

Answer

3π

Answer

4π

Question 25

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 26

What is the value of sin(π/3)?

Accepted Answer

√3/2

Answer

1/2

Answer

√2/2

Answer

1

Question 27

What is the domain of the function f(x) = tan(x)?

Accepted Answer

{x | x ≠ nπ/2, n ∈ Z}

Answer

{x | x ≠ nπ, n ∈ Z}

Answer

R

Answer

{x | x ≠ 0}

Question 28

Find the vertical shift of the function y = 2cos(x) + 1.

Accepted Answer

1

Answer

2

Answer

4

Answer

π

Question 29

Which trigonometric identity is used to find the value of cos(π/2 - x)?

Accepted Answer

Cosine difference identity

Answer

Pythagorean identity

Answer

Sine double-angle identity

Answer

Tangent half-angle identity

Question 30

What is the domain of the function y = csc(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 31

The amplitude of the function y = -3cos(2x) is:

Accepted Answer

3

Answer

1

Answer

2

Answer

6

Question 32

The value of sin(π/4) + cos(π/3) is:

Accepted Answer

√2

Answer

0

Answer

1

Answer

2

Question 33

Which of the following precisely defines the sine function?

Accepted Answer

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Answer

The sine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.

Answer

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.

Answer

The sine of an angle is the ratio of the length of the hypotenuse to the length of the side opposite the angle.

Question 34

Which of the following trigonometric identities is correct?

Accepted Answer

sin²θ + cos²θ = 1

Answer

sin²θ + cos²θ = 0

Answer

tan²θ + cot²θ = 1

Answer

sinθ + cosθ = 1

Question 35

The function f(x) = 2sin(3x) has an amplitude of:

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 36

Identify the period of the sine function.

Accepted Answer

2π

Answer

π

Answer

4π

Answer

6π

Question 37

Select an example of a trigonometric identity:

Accepted Answer

sin²x + cos²x = 1

Answer

tanx = sinx / cosx

Answer

cotx = 1 / tanx

Answer

secx = tanx / cosx

Question 38

Evaluate sin(π/6).

Accepted Answer

√3/2

Answer

0

Answer

1/2

Answer

1

Question 39

Express tan(π - x) in terms of tanx.

Accepted Answer

-tanx

Answer

tanx

Answer

1 / tanx

Answer

-1 / tanx

Question 40

Identify the reciprocal identity for sine.

Accepted Answer

sin(x) = 1/cos(x)

Answer

sin(x) = 1/tan(x)

Answer

sin(x) = 1/cot(x)

Answer

sin(x) = 1/sec(x)

Question 41

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

Accepted Answer

x = cos⁻¹(y)

Answer

x = sin(y)

Answer

x = tan(y)

Answer

x = cot(y)

Question 42

Which trigonometric function is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 43

What is the range of values that the sine function can take on?

Accepted Answer

[-1, 1]

Answer

[0, 1]

Answer

[1, ∞]

Answer

[-∞, ∞]

Question 44

What is the period of the cosine function?

Accepted Answer

2π

Answer

π

Answer

4π

Answer

6π

Question 45

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

Accepted Answer

A graph of y = sin(x) reflected over the x-axis

Answer

A graph of y = sin(x) shifted down by 1 unit

Answer

A graph of y = sin(x) shifted up by 1 unit

Answer

A graph of y = sin(x) reflected over the y-axis

Question 46

Which of the following functions is NOT included in the Unit Circle?

Accepted Answer

Arccosine

Answer

Sine

Answer

Cosine

Answer

Tangent

Question 47

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 48

Which of the following equations represents the sine function with an amplitude of 3 and a period of π?

Accepted Answer

y = 3sin(2x)

Answer

y = 3sin(x)

Answer

y = sin(3x)

Answer

y = sin(2πx)

Question 49

What is the value of sin(π/3)?

Accepted Answer

√3/2

Answer

-1/2

Answer

1/2

Answer

-√3/2

Question 50

Solve the equation 2sin(x) - 1 = 0 for 0 ≤ x < 2π.

Accepted Answer

π/6, 5π/6

Answer

π/4, 3π/4

Answer

π/3, 2π/3

Answer

0, π