AP PreCalculus Flashcards: Sine, Cosine, and Tangent
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
Define an angle in 'standard position' on the coordinate plane.
An angle is in standard position when its vertex is at the origin and one ray coincides with the positive x-axis.
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Define an angle in 'standard position' on the coordinate plane.
An angle is in standard position when its vertex is at the origin and one ray coincides with the positive x-axis.
If an angle's terminal ray intersects the unit circle at a point P(x, y), what trigonometric function does the y-coordinate represent?
The y-coordinate represents the sine of the angle.
Tangent (using the unit circle)
The tangent of an angle is the ratio of the y-coordinate to the x-coordinate (y/x) of the point where the terminal ray intersects the unit circle.
Given that sin(θ) = y and cos(θ) = x for a point on the unit circle, what is the alternate formula for tan(θ)?
The tangent of the angle is the ratio of the angle's sine to its cosine (tan(θ) = sin(θ)/cos(θ)).
Sine (using the unit circle)
For a unit circle, the sine of an angle is the y-coordinate of the point where the terminal ray intersects the circle.
What two lengths form the ratio that defines radian measure?
Radian measure is the ratio of the length of the arc of a circle to the radius of that same circle.
Given the intersection point P(x, y) on the unit circle for an angle, how do you calculate the tangent?
The tangent is calculated as the ratio of the y-coordinate to the x-coordinate, which is y/x.
Cosine (using the unit circle)
For a unit circle, the cosine of an angle is the x-coordinate of the point where the terminal ray intersects the circle.
How can the tangent of an angle be expressed in terms of its sine and cosine?
The tangent of an angle is the ratio of the angle's sine to its cosine.
What is the primary tool mentioned for determining sine, cosine, and tangent from coordinates?
The unit circle is used to determine the sine, cosine, and tangent of an angle.
How is the radian measure of an angle in standard position defined?
It is the ratio of the length of the arc subtended by the angle to the radius of the circle centered at the origin.
On a unit circle, how are the sine and cosine of an angle determined by the coordinates of a point P?
The sine of the angle is the y-coordinate of point P, and the cosine is the x-coordinate of point P, where the terminal ray intersects the circle.
If an angle's terminal ray intersects the unit circle at a point P(x, y), what trigonometric function does the x-coordinate represent?
The x-coordinate represents the cosine of the angle.
What two conditions must be met for an angle to be in standard position?
The angle's vertex must coincide with the origin, and one of its rays must coincide with the positive x-axis.