AP®︎ Precalculus: Topic 3.2 Practice Test
Prepare for your quiz, test, or the AP exam with focused practice questions on Topic 3.2 of AP Precalculus – Sine, Cosine, and Tangent.
Questions List
Topic 3.2
Question 1 Easy
Which of the following shows an angle in standard position?
What You’re Being Tested On:
Explore the learning objectives taken directly from the College Board’s AP® Precalculus Curriculum. Ensure you’re prepared for the exact topics covered on the AP® exam, in-class tests, and quizzes, and gain confidence in your mastery of the material.
Topic 3.2: Sine, Cosine, and Tangent
Learning Objective: 3.2.A
Determine the sine, cosine, and tangent of an angle using the unit circle.
Essential Knowledge: 3.2.A.1
In the coordinate plane, an angle is in standard position when the vertex coincides with the origin and one ray coincides with the positive -axis. The other ray is called the terminal ray. Positive and negative angle measures indicate rotations from the positive -axis in the counterclockwise and clockwise direction, respectively. Angles in standard position that share a terminal ray differ by an integer number of revolutions.
Essential Knowledge: 3.2.A.2
When considering a circle centered at the origin, the radian measure of an angle in standard position is the ratio of the length of the arc of the circle that the angle subtends to the radius of that same circle. For a unit circle, which has radius 1, one radian is the measure of the angle subtended at the center of the circle by an arc that has length 1.
Essential Knowledge: 3.2.A.3
Given an angle in standard position and a circle centered at the origin, there is a point, , where the terminal ray intersects the circle. The sine of the angle is the ratio of the vertical displacement of from the -axis to the distance between the origin and point . Therefore, for a unit circle, the sine of the angle is the -coordinate of point .
Essential Knowledge: 3.2.A.4
Given an angle in standard position and a circle centered at the origin, there is a point, , where the terminal ray intersects the circle. The cosine of the angle is the ratio of the horizontal displacement of from the -axis to the distance between the origin and point . Therefore, for a unit circle, the cosine of the angle is the -coordinate of point .
Essential Knowledge: 3.2.A.5
Given an angle in standard position, the tangent of the angle is the slope, if it exists, of the terminal ray. Because the slope of the terminal ray is the ratio of the vertical displacement to the horizontal displacement over any interval, the tangent of the angle is the ratio of the -coordinate to the -coordinate of the point at which the terminal ray intersects the unit circle; alternately, it is the ratio of the angle’s sine to its cosine.
