Sinusoidal Functions

Flashcard
•
Mathematics
•
10th - 11th Grade
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a sinusoidal function?
Back
A sinusoidal function is a mathematical function that describes a smooth, periodic oscillation. It can be represented by sine or cosine functions, such as y = sin(x) or y = cos(x).
Tags
CCSS.HSF.TF.A.4
2.
FLASHCARD QUESTION
Front
What is the general form of a sinusoidal function?
Back
The general form of a sinusoidal function is y = a sin(bx - c) + d or y = a cos(bx - c) + d, where 'a' is the amplitude, 'b' affects the period, 'c' is the phase shift, and 'd' is the vertical shift.
Tags
CCSS.HSF-IF.C.7E
3.
FLASHCARD QUESTION
Front
How do you find the amplitude of a sinusoidal function?
Back
The amplitude of a sinusoidal function is the absolute value of 'a' in the equation y = a sin(bx - c) + d or y = a cos(bx - c) + d. It represents the maximum distance from the midline to the peak.
Tags
CCSS.HSF-IF.C.7E
4.
FLASHCARD QUESTION
Front
What is the period of a sinusoidal function?
Back
The period of a sinusoidal function is the distance (in terms of x) it takes for the function to complete one full cycle. It can be calculated using the formula P = \frac{2\pi}{|b|}, where 'b' is the coefficient of x.
Tags
CCSS.HSF.TF.A.4
5.
FLASHCARD QUESTION
Front
What is the phase shift in a sinusoidal function?
Back
The phase shift of a sinusoidal function is the horizontal shift left or right in the graph. It is determined by the value of 'c' in the equation y = a sin(bx - c) + d or y = a cos(bx - c), calculated as \frac{c}{b}.
Tags
CCSS.HSF-IF.C.7E
6.
FLASHCARD QUESTION
Front
What is the vertical shift in a sinusoidal function?
Back
The vertical shift of a sinusoidal function is the amount by which the graph is shifted up or down. It is represented by 'd' in the equation y = a sin(bx - c) + d or y = a cos(bx - c).
Tags
CCSS.HSF-IF.C.7E
7.
FLASHCARD QUESTION
Front
How do you determine if a function is sine or cosine?
Back
To determine if a function is sine or cosine, observe the starting point of the graph. A sine function starts at the midline (0) and goes up, while a cosine function starts at its maximum value (a).
Tags
CCSS.HSF-IF.C.7E
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