AP PreCalculus Flashcards: Sine and Cosine Function Graphs
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
For a point P on the unit circle, which function represents its horizontal displacement from the y-axis?
The cosine function, f(θ) = cos θ, represents the horizontal displacement from the y-axis.
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For a point P on the unit circle, which function represents its horizontal displacement from the y-axis?
The cosine function, f(θ) = cos θ, represents the horizontal displacement from the y-axis.
How are representations of the sine and cosine functions constructed?
Representations of the sine and cosine functions are constructed by using the coordinates of a point as it moves around the unit circle.
What is the sine function, f(θ) = sin θ, in the context of the unit circle?
The sine function gives the y-coordinate, or vertical displacement from the x-axis, of a point P on the unit circle.
Describe the behavior of the output values for the cosine function as its input values increase.
As the input values of the cosine function increase, the output values oscillate, or vary repetitively, between -1 and 1.
Describe the behavior of the output values for the sine function as its input values increase.
As the input values of the sine function increase, the output values oscillate, or vary repetitively, between -1 and 1.
If a point P on the unit circle corresponds to an angle θ, what are its (x, y) coordinates in terms of trigonometric functions?
The coordinates of point P are (cos θ, sin θ), where the x-coordinate is given by the cosine function and the y-coordinate is given by the sine function.
Term: Oscillation (in trigonometry)
Oscillation refers to the repetitive variation of the output values of the sine and cosine functions between the minimum value of -1 and the maximum value of 1.
Why are the output values of sine and cosine functions restricted to the interval [-1, 1]?
The outputs are restricted because they represent the x and y coordinates of a point on the unit circle, which has a radius of 1, making it impossible for a coordinate to be greater than 1 or less than -1.
What is the range of the sine and cosine functions?
Both the sine and cosine functions have output values that oscillate between -1 and 1, inclusive. The range is [-1, 1].
What is the cosine function, f(θ) = cos θ, in the context of the unit circle?
The cosine function gives the x-coordinate, or horizontal displacement from the y-axis, of a point P on the unit circle.
For a point P on the unit circle, which function represents its vertical displacement from the x-axis?
The sine function, f(θ) = sin θ, represents the vertical displacement from the x-axis.