AP PreCalculus Practice Quiz: Sine and Cosine Function Graphs

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 11 questions to check your progress.

Question 1 of 11

According to the provided content, the sine function, f(θ) = sin θ, is derived from the unit circle and represents which of the following?

A)The x-coordinate of a point P on the circle.B)The y-coordinate of a point P on the circle.C)The radius of the circle.D)The circumference of the circle.

All Questions (11)

According to the provided content, the sine function, f(θ) = sin θ, is derived from the unit circle and represents which of the following?

A) The x-coordinate of a point P on the circle.

B) The y-coordinate of a point P on the circle.

C) The radius of the circle.

D) The circumference of the circle.

Correct Answer: B

The content explicitly states that the sine function, f(θ) = sin θ, gives the y-coordinate of point P on the unit circle.

The cosine function, f(θ) = cos θ, is defined in relation to the unit circle. What does it measure?

A) The vertical displacement from the x-axis.

B) The horizontal displacement from the y-axis.

C) The distance from the origin to the point P.

D) The angle θ in radians.

Correct Answer: B

The provided text defines the cosine function as giving the x-coordinate, which is the horizontal displacement from the y-axis, of a point P on the unit circle.

What is the range of output values for the sine function, f(θ) = sin θ, as the input values increase?

A) The values oscillate between 0 and 1.

B) The values increase infinitely.

C) The values oscillate between -1 and 1.

D) The values are always positive.

Correct Answer: C

The content states that as the input values of the sine function increase, the output values oscillate between -1 and 1.

Based on its definition using the unit circle, what are the minimum and maximum values for the cosine function, f(θ) = cos θ?

A) Minimum 0, Maximum 1

B) Minimum -1, Maximum 1

C) Minimum -∞, Maximum ∞

D) Minimum 0, Maximum 2π

Correct Answer: B

The text specifies that as the input values of the cosine function increase, the output values oscillate between -1 and 1.

For a point P on the unit circle, the vertical displacement from the x-axis is given by which function?

A) f(θ) = cos θ

B) f(θ) = tan θ

C) f(θ) = sin θ

D) f(θ) = θ

Correct Answer: C

The content defines the sine function, f(θ) = sin θ, as giving the y-coordinate, which represents the vertical displacement from the x-axis.

If a point P is on the unit circle, its x-coordinate corresponds to the output of which trigonometric function?

A) The sine function

B) The cosine function

C) Both the sine and cosine functions

D) Neither the sine nor cosine function

Correct Answer: B

The provided text states that the cosine function, f(θ) = cos θ, gives the x-coordinate of point P on the unit circle.

What fundamental geometric shape is used to construct representations of the sine and cosine functions?

A) A right triangle

B) A square

C) The unit circle

D) A parabola

Correct Answer: C

The first point of the provided content explicitly states that representations of the sine and cosine functions are constructed using the unit circle.

The oscillating nature of the sine and cosine functions between -1 and 1 is a direct consequence of their definition based on:

A) The coordinates of a point P on a circle with a radius of 1.

B) The ever-increasing angle θ.

C) The properties of right triangles with a hypotenuse of 2.

D) The ratio of a circle's circumference to its diameter.

Correct Answer: A

The functions are defined as the x and y coordinates of a point on the unit circle. Since the radius is 1, the x and y coordinates cannot be less than -1 or greater than 1, causing the oscillation between these values.

Which statement accurately describes the output values of the cosine function?

A) They represent the y-coordinate and range from 0 to 1.

B) They represent the x-coordinate and increase without bound.

C) They represent the y-coordinate and oscillate between -1 and 1.

D) They represent the x-coordinate and oscillate between -1 and 1.

Correct Answer: D

The content specifies that the cosine function gives the x-coordinate (horizontal displacement) and that its output values oscillate between -1 and 1.

Which statement accurately describes the output values of the sine function?

A) They represent the y-coordinate and oscillate between -1 and 1.

B) They represent the x-coordinate and oscillate between -1 and 1.

C) They represent the y-coordinate and are always non-negative.

D) They represent the x-coordinate and decrease infinitely.

Correct Answer: A

The content specifies that the sine function gives the y-coordinate (vertical displacement) and that its output values oscillate between -1 and 1.

A point P moves along the unit circle. The measure of its horizontal displacement from the y-axis is tracked. This measurement directly corresponds to the values of which function?

A) f(θ) = sin θ, because it measures vertical position.

B) f(θ) = cos θ, because it measures vertical position.

C) f(θ) = sin θ, because it is defined by the x-coordinate.

D) f(θ) = cos θ, because it is defined by the x-coordinate.

Correct Answer: D

The content states that the cosine function, f(θ) = cos θ, gives the x-coordinate, which is the horizontal displacement from the y-axis. Therefore, tracking this measurement corresponds to the cosine function.