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AP PreCalculus Practice Quiz: Sine, Cosine, and Tangent

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

Test your understanding with short quizzes. This quiz has 12 questions to check your progress.

Question 1 of 12

According to the provided text, when is an angle in the coordinate plane considered to be in standard position?

All Questions (12)

According to the provided text, when is an angle in the coordinate plane considered to be in standard position?

A) When its vertex is at the origin and one ray is on the positive x-axis.

B) When its vertex is at the origin and one ray is on the positive y-axis.

C) When the angle measures 90 degrees.

D) When its terminal ray intersects the unit circle at (1, 0).

Correct Answer: A

The text states, 'In the coordinate plane, an angle is in standard position when the vertex coincides with the origin and one ray coincides with the positive x-axis.'

For an angle whose terminal ray intersects a unit circle at point P, what does the sine of the angle represent?

A) The x-coordinate of point P.

B) The y-coordinate of point P.

C) The ratio of the y-coordinate to the x-coordinate of point P.

D) The length of the arc from the positive x-axis to point P.

Correct Answer: B

The content specifies, 'For a unit circle, the sine of the angle is the y-coordinate of point P, where the terminal ray intersects the circle.'

For an angle whose terminal ray intersects a unit circle at point P, what does the cosine of the angle represent?

A) The y-coordinate of point P.

B) The ratio of the x-coordinate to the y-coordinate of point P.

C) The x-coordinate of point P.

D) The radius of the circle.

Correct Answer: C

The content states, 'For a unit circle, the cosine of the angle is the x-coordinate of point P, where the terminal ray intersects the circle.'

What is the definition of the radian measure of an angle in standard position?

A) The length of the arc subtended by the angle on a unit circle.

B) The ratio of the circle's radius to the length of the arc subtended by the angle.

C) The ratio of the length of the subtended arc to the radius of the circle.

D) The y-coordinate of the point where the terminal ray intersects the circle.

Correct Answer: C

The text defines radian measure as 'the ratio of the length of the arc of a circle centered at the origin subtended by the angle to the radius of that same circle.'

The terminal ray of an angle θ intersects the unit circle at a point P with coordinates (x, y). Which of the following correctly defines the tangent of θ?

A) The product of the x-coordinate and the y-coordinate.

B) The x-coordinate divided by the y-coordinate.

C) The ratio of the angle's sine to its cosine.

D) The y-coordinate divided by the sine of the angle.

Correct Answer: C

The content provides two equivalent definitions for tangent: 'the ratio of the y-coordinate to the x-coordinate' and 'alternately, it is the ratio of the angle's sine to its cosine.' Option C is one of these correct definitions.

An angle in standard position has a terminal ray that intersects the unit circle at the point P(0.6, 0.8). What is the sine of this angle?

A) 0.6

B) 0.8

C) 1.0

D) 1.33

Correct Answer: B

Based on the provided content, the sine of an angle on the unit circle is the y-coordinate of the intersection point P. For P(0.6, 0.8), the y-coordinate is 0.8.

An angle in standard position has a terminal ray that intersects the unit circle at the point P(-0.5, √3/2). What is the cosine of this angle?

A) -0.5

B) √3/2

C) -√3

D) 1

Correct Answer: A

The content states that the cosine of an angle on the unit circle is the x-coordinate of the intersection point P. For P(-0.5, √3/2), the x-coordinate is -0.5.

The terminal ray of an angle θ in standard position intersects the unit circle at the point P(-√2/2, -√2/2). What is the tangent of θ?

A) -1

B) 0

C) 1

D) Undefined

Correct Answer: C

The tangent is defined as the ratio of the y-coordinate to the x-coordinate (y/x). In this case, tan(θ) = (-√2/2) / (-√2/2) = 1.

Given that the terminal ray of an angle θ intersects the unit circle at point P(x, y), which of the following expressions is equivalent to tan(θ)?

A) cos(θ) / sin(θ)

B) sin(θ) / cos(θ)

C) sin(θ) * cos(θ)

D) 1 / sin(θ)

Correct Answer: B

The content explicitly states that the tangent of an angle is 'the ratio of the angle's sine to its cosine.'

The terminal ray of an angle θ in standard position intersects the unit circle at a point P whose coordinates are (c, d). Based on the provided definitions, what is sin(θ)?

A) c

B) d

C) d/c

D) c/d

Correct Answer: B

The definition of sine for an angle on the unit circle is the y-coordinate of the intersection point. For a point P(c, d), the y-coordinate is d.

If sin(θ) = m and cos(θ) = n for an angle θ whose terminal ray intersects the unit circle, which expression represents tan(θ)?

A) n / m

B) m * n

C) m / n

D) m - n

Correct Answer: C

The content defines tangent as the ratio of the angle's sine to its cosine. Therefore, tan(θ) = sin(θ) / cos(θ) = m / n.

An angle's terminal ray intersects the unit circle at point P(0, 1). According to the provided definitions, what is the tangent of this angle?

A) 0

B) 1

C) -1

D) Undefined

Correct Answer: D

The tangent is defined as the ratio of the y-coordinate to the x-coordinate (y/x). For the point P(0, 1), this ratio is 1/0. Division by zero is undefined.