Master Trigonometric Functions: Online Quizzes and Practice

Question 1

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

Accepted Answer

2π/3

Answer

π/2

Answer

π/3

Answer

π

Question 2

Represent the vertical translation of the function y = cosx by 2 units upward as an equation.

Accepted Answer

y = cosx + 2

Answer

y = cosx - 2

Answer

y = 2cosx

Answer

y = cos(2x)

Question 3

Which method cannot be used to solve a trigonometric equation?

Accepted Answer

Quadratic formula

Answer

Factoring

Answer

Double-angle identities

Answer

Substitution

Question 4

Find the general solution of the equation 2sin²x - 1 = 0.

Accepted Answer

x = nπ/2

Answer

x = nπ

Answer

x = nπ/4

Answer

x = nπ/6

Question 5

Which of the following trigonometric functions is an even function?

Accepted Answer

cosine

Answer

sine

Answer

tangent

Answer

cotangent

Question 6

Which trigonometric identity is used to simplify expressions involving the sine and cosine of double angles?

Accepted Answer

Double-angle identity

Answer

Sum-to-product identity

Answer

Product-to-sum identity

Answer

Pythagorean identity

Question 7

Which of the following functions is periodic with a period of 2π?

Accepted Answer

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

Answer

y = tan(x) - sec(x)

Answer

y = cot(2x) + csc(x)

Answer

y = sin(x) * cos(x)

Question 8

Which trigonometric identity is equivalent to 1?

Accepted Answer

sin²θ + cos²θ

Answer

tan²θ - 1

Answer

sec²θ - 1

Answer

csc²θ - cot²θ

Question 9

Describe the transformation of the function g(x) = 2sin(x - π/4) compared to the parent sine function.

Accepted Answer

Shifted π/4 units to the left

Answer

Shifted π/4 units to the right

Answer

Amplitude stretched by a factor of 2

Answer

Period compressed by a factor of 2

Question 10

Which trigonometric function is odd?

Accepted Answer

sin(x)

Answer

cos(x)

Answer

tan(x)

Answer

cot(x)

Question 11

What is the domain of the function k(x) = 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 π/2

Question 12

What is the inverse function of sin(x)?

Accepted Answer

arcsin(x)

Answer

arccos(x)

Answer

arctan(x)

Answer

arccot(x)

Question 13

Which of the following trigonometric identities is valid?

Accepted Answer

sin²θ - cos²θ = 1

Answer

sin²θ + cos²θ = 0

Answer

sin(θ + π) = sinθ + cosθ

Answer

cos(θ - π) = cosθ - sinθ

Question 14

Use trigonometric identities to simplify the expression: cos²x - sin²x.

Accepted Answer

cos2x

Answer

sin2x

Answer

-cos2x

Answer

-sin2x

Question 15

In a right triangle with sides a, b, and c, where c is the hypotenuse, which of the following represents the Pythagorean theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c

Answer

c² - a² = b

Answer

c² + a² = b

Question 16

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

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 17

Which of the following identities is used to convert a sum of cosine functions into a product?

Accepted Answer

cos(A + B) = cos(A) * cos(B) - sin(A) * sin(B)

Answer

sin(A + B) = sin(A) * cos(B) + cos(A) * sin(B)

Answer

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

Answer

cot(A + B) = (cot(A) * cot(B) - 1) / (cot(A) + cot(B))

Question 18

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

Accepted Answer

All real numbers except multiples of π/2

Answer

All real numbers

Answer

All real numbers except 0

Answer

Only positive real numbers

Question 19

What is the inverse function of the sine function?

Accepted Answer

arcsine

Answer

arcosine

Answer

arctangent

Answer

arccotangent

Question 20

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

Accepted Answer

2 * cos(2x)

Answer

cos(2x)

Answer

-2 * cos(2x)

Answer

-cos(2x)

Question 21

On the unit circle, what is the exact value of the sine of pi over 12?

Accepted Answer

√3 / 2

Answer

1 / 2

Answer

√2 / 2

Question 22

What is the range of the function y = -2cos(x) + 3?

Accepted Answer

[-1, 5]

Answer

[-3, 3]

Answer

[1, 5]

Answer

[-5, 1]

Question 23

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

Accepted Answer

cosecant

Answer

sine

Answer

cosine

Answer

tangent

Question 24

Prove the trigonometric identity: cos(2θ) = cos²θ - sin²θ.

Accepted Answer

cos(2θ) = cos²θ - sin²θ

Answer

cos(2θ) = cos²θ + sin²θ

Answer

cos(2θ) = 2cos²θ - 1

Answer

cos(2θ) = 1 - 2sin²θ

Question 25

Which trigonometric function is odd?

Accepted Answer

Sine

Answer

Cosine

Answer

Tangent

Answer

Cotangent

Question 26

Which of the following trigonometric identities is true?

Accepted Answer

sin²(x) + cos²(x) = 1

Answer

tan²(x) - 1 = sin²(x)

Answer

cot(x) = tan(x) - 1

Answer

cos(x) - sin(x) = 1

Question 27

The inverse function of cosine is:

Accepted Answer

Arccosine

Answer

Sine

Answer

Tangent

Answer

Arctangent

Question 28

Which of the following identities is true for trigonometric functions?

Accepted Answer

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

Answer

tan(x) = sin(x) + cos(x)

Answer

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

Answer

cot(x) = tan(x) - 1

Question 29

The period of the sine function is:

Accepted Answer

2π

Answer

π

Answer

π/2

Answer

3π/2

Question 30

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

Accepted Answer

2

Answer

1

Answer

3

Answer

6

Question 31

Which of the following describes the asymptotes of the graph of y = tan(x)?

Accepted Answer

Vertical asymptotes at x = π/2 + πn

Answer

Horizontal asymptotes at y = ±1

Answer

No asymptotes

Answer

Horizontal asymptotes at y = 0

Question 32

What is the range of the sine function?

Accepted Answer

(-1, 1)

Answer

(0, 1)

Answer

(-∞, ∞)

Answer

(1, ∞)

Question 33

Identify the trigonometric identity that is NOT valid:

Accepted Answer

secx = cosx / tanx

Answer

sin²x + cos²x = 1

Answer

tanx = sinx / cosx

Answer

cscx = 1 / sinx

Question 34

Solve for x: 2sinx - 1 = 0

Accepted Answer

x = π/6, 5π/6

Answer

x = π/4, 3π/4

Answer

x = π/2, π

Answer

x = 0, π

Question 35

Name the inverse function of the cosine function:

Accepted Answer

arccosine

Answer

arcsine

Answer

arctangent

Answer

arccotangent

Question 36

Describe the most straightforward method for finding the exact value of cos(5π/6):

Accepted Answer

Use the unit circle

Answer

Use the sum-to-product formula

Answer

Use the half-angle formula

Answer

Use the Pythagorean identity

Question 37

The period of the function y = cos(2x) indicates:

Accepted Answer

The time it takes for the function to complete one full cycle

Answer

The vertical distance between the maximum and minimum points

Answer

The amplitude of the function

Answer

The phase shift of the function

Question 38

To solve the trigonometric equation 2sin(x) - 1 = 0, what strategy should you use?

Accepted Answer

Using the inverse sine function

Answer

Factoring

Answer

Applying the Pythagorean identity

Answer

Graphical representation

Question 39

The amplitude of a trigonometric function determines:

Accepted Answer

The vertical stretch or compression of the graph

Answer

The horizontal shift of the graph

Answer

The vertical shift of the graph

Answer

The period of the graph

Question 40

Which type of curve is represented by the graph of y = tan(x) in the interval [-pi/2, pi/2]?

Accepted Answer

A parabola

Answer

A straight line

Answer

A circle

Answer

A hyperbola

Question 41

The inverse function of y = cos(x) is used to:

Accepted Answer

Find the angle whose cosine is a given value

Answer

Find the cosine of an angle whose value is given

Answer

Solve trigonometric equations

Answer

Graph trigonometric functions

Question 42

When differentiating the function y = sin(x^2), which rule of differentiation should be applied?

Accepted Answer

Chain rule

Answer

Power rule

Answer

Product rule

Answer

Quotient rule

Question 43

In a sector of a circle, the area is calculated using the formula:

Accepted Answer

Area = 1/2 * radius^2 * central angle (in radians)

Answer

Area = radius^2 * central angle (in degrees)

Answer

Area = 1/2 * radius * central angle (in radians)

Answer

Area = radius * central angle (in degrees)

Question 44

Precisely define the period of the sine function.

Accepted Answer

2π

Answer

π

Answer

3π

Answer

4π

Question 45

Identify the trigonometric identity employed to convert a sum of sines and cosines into a single sine or cosine function.

Accepted Answer

Sum-to-Product Identity

Answer

Product-to-Sum Identity

Answer

Double-Angle Identity

Answer

Half-Angle Identity

Question 46

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

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 47

Which of the following equations possesses a solution within the interval [0, 2π)?

Accepted Answer

cos(x) = 0

Answer

sin(x) = -1

Answer

tan(x) is undefined

Answer

sec(x) = 0

Question 48

State the range of the trigonometric function y = tan(x).

Accepted Answer

(-∞, ∞)

Answer

(-∞, -1)

Answer

(-1, 1)

Answer

(1, ∞)

Question 49

Identify the trigonometric identity specifically employed to solve trigonometric equations involving the double angle.

Accepted Answer

Double-Angle Identity

Answer

Half-Angle Identity

Answer

Sum-to-Product Identity

Answer

Product-to-Sum Identity

Question 50

What is the period of the sine function?

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

4π

Question 51

Determine the period of the function: f(x) = tan(2x + π/4).

Accepted Answer

2π

Answer

π/2

Answer

π

Answer

π/4

Question 52

Identify the amplitude of the trigonometric function: g(θ) = -3sin(4θ).

Accepted Answer

-3

Answer

3

Answer

4

Answer

-4

Question 53

Find the inverse of the function y = sec x.

Accepted Answer

y = arcsec x

Answer

y = arcsin x

Answer

y = arccos x

Answer

y = arctan x

Question 54

Which of the following is a Pythagorean identity?

Accepted Answer

sin² x + cos² x = 1

Answer

tan² x + 1 = sec² x

Answer

cot² x - 1 = csc² x

Answer

sin x + cos x = 1

Question 55

The period of the trigonometric sine function is:

Accepted Answer

2π

Answer

0.5π

Answer

π

Answer

4π

Question 56

Evaluate sin(π/2).

Accepted Answer

1

Answer

-1

Answer

0

Answer

undefined

Question 57

Find the derivative of cos(x).

Accepted Answer

-sin(x)

Answer

sin(x)

Answer

cos(x)

Answer

-cos(x)

Question 58

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

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 59

What is the inverse function of the tangent function?

Accepted Answer

arctangent

Answer

arcsine

Answer

arccosine

Answer

arccotangent

Question 60

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

Accepted Answer

A graph with vertical asymptotes at x = 0 and x = π.

Answer

A graph with a horizontal asymptote at y = 1.

Answer

A graph with a period of π.

Answer

A graph that oscillates between y = -1 and y = 1.

Question 61

What is the derivative of the function y = csc(x)?

Accepted Answer

-csc(x)cot(x)

Answer

csc^2(x)

Answer

-tan(x)

Answer

-cot(x)

Question 62

Which of the following applications of trigonometry is used to find the distance between two points on a map?

Accepted Answer

Solving a right triangle

Answer

Finding the area of a triangle

Answer

Finding the volume of a sphere

Answer

Calculating the circumference of a circle

Question 63

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

Accepted Answer

(-∞, -1] ∪ [1, ∞)

Answer

All real numbers

Answer

All integers

Answer

[-1, 1]

Question 64

If the value of sine of an angle θ is 0.5, what is the value of cosine of θ?

Accepted Answer

0.87

Answer

0.5

Answer

1.73

Answer

2