AP PreCalculus Flashcards: Sinusoidal Function Transformations
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 16 cards to help you master important concepts.
In the general form f(θ) = a sin(b(θ+c)) + d, what does the parameter 'd' represent?
The parameter 'd' represents a vertical shift of the graph's midline by d units from y=0.
Card 1 of 16
All Flashcards (16)
In the general form f(θ) = a sin(b(θ+c)) + d, what does the parameter 'd' represent?
The parameter 'd' represents a vertical shift of the graph's midline by d units from y=0.
What are sinusoidal functions?
Functions that can be written in the form f(θ) = a sin(b(θ+c)) + d or g(θ) = a cos(b(θ+c)) + d are sinusoidal functions.
Define Period for the function y = a sin(b(θ+c)) + d.
The period is the length of one full cycle, calculated as |1/b| * 2π units.
How does the parameter 'b' in g(θ) = sin(bθ) affect the graph?
It causes a horizontal dilation of the graph and changes the period by a factor of |1/b|.
What type of transformation is described by g(θ) = sin(θ) + d?
This additive transformation is a vertical translation of the graph of f, including its midline, by d units.
In the general form f(θ) = a sin(b(θ+c)) + d, what does the parameter 'c' represent?
The parameter 'c' represents a horizontal translation, or phase shift, of the graph by -c units.
For the function f(θ) = sin(θ/2), how does the period differ from the parent function f(θ) = sin(θ)?
The period differs by a factor of |1/b|, which is |1/(1/2)|, or a factor of 2.
Identify the vertical shift for the function f(θ) = 2 sin(θ) - 8.
The vertical shift is d units, which is a shift of -8 units from y=0.
Define Amplitude for the function y = a sin(b(θ+c)) + d.
The amplitude is the vertical dilation of the graph, given by the value |a| units.
Define Vertical Shift for the function y = a sin(b(θ+c)) + d.
The vertical shift is the translation of the graph's midline by d units from y=0.
Define Phase Shift for the function y = a sin(b(θ+c)) + d.
The phase shift is the horizontal translation of the graph, given by the value -c units.
What is the amplitude of the function f(θ) = -5 sin(2(θ - 1)) + 3?
The amplitude is |a|, which is |-5|, or 5 units.
Identify the phase shift for the function g(θ) = 3 cos(θ + π/3).
The phase shift is -c units, which is a shift of -π/3 units.
What is the period of the function g(θ) = cos(4(θ + π)) - 1?
The period is |1/b| * 2π, which is |1/4| * 2π, or π/2 units.
How does the parameter 'a' in g(θ) = a sin(θ) affect the graph?
It causes a vertical dilation of the graph and changes the amplitude by a factor of |a|.
What are the four key parameters to identify in a sinusoidal function transformation?
The four key parameters to identify are the amplitude, vertical shift, period, and phase shift.