AP PreCalculus Flashcards: Sinusoidal Functions
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.
What type of symmetry does the graph of y = sin θ exhibit?
The graph of y = sin θ is an odd function, meaning it is symmetric with respect to the origin.
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What type of symmetry does the graph of y = sin θ exhibit?
The graph of y = sin θ is an odd function, meaning it is symmetric with respect to the origin.
Period
The period of a sinusoidal function is the horizontal length of one complete cycle; it is the reciprocal of the frequency.
What is a sinusoidal function?
A sinusoidal function is any function that involves additive and multiplicative transformations of f(θ) = sin θ.
What type of symmetry does the graph of y = cos θ exhibit?
The graph of y = cos θ is an even function, meaning it is symmetric with respect to the y-axis.
Frequency
The frequency of a sinusoidal function is the number of cycles it completes in a given interval; it is the reciprocal of the period.
Define the amplitude of a sinusoidal function.
The amplitude of a sinusoidal function is half the difference between its maximum and minimum values.
How do you calculate the amplitude of a sinusoidal function given its maximum and minimum values?
To find the amplitude, calculate half the difference between the maximum and minimum values of the function.
Identify a key characteristic of the cosine function's graph.
The graph of the parent cosine function, y = cos θ, is an even function that has a maximum value at its y-intercept (0,1).
What is the relationship between the period and frequency of a sinusoidal function?
The period and frequency of a sinusoidal function are reciprocals of each other.
What is an even function?
An even function is one whose graph is symmetric with respect to the y-axis, such as y = cos θ.
Identify a key characteristic of the sine function's graph.
The graph of the parent sine function, y = sin θ, is an odd function that passes through the origin (0,0).
What is the midline of a sinusoidal function's graph?
The midline is the horizontal line determined by the average of the maximum and minimum values of the function.
How do you determine the equation of the midline from a function's maximum and minimum values?
The midline is found by calculating the average, or arithmetic mean, of the maximum and minimum values.
What is an odd function?
An odd function is one whose graph is symmetric with respect to the origin, such as y = sin θ.