Sin/Cos & amplititude

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the amplitude of a sine or cosine function?
Back
The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.
2.
FLASHCARD QUESTION
Front
What is the general form of a sine function?
Back
The general form is: y = A sin(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.
3.
FLASHCARD QUESTION
Front
What is the general form of a cosine function?
Back
The general form is: 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.
4.
FLASHCARD QUESTION
Front
How do you determine the amplitude from the equation y = -4 cos(5x)?
Back
The amplitude is the absolute value of A. Here, A = -4, so the amplitude is | -4 | = 4.
5.
FLASHCARD QUESTION
Front
What is the period of a sine or cosine function?
Back
The period is the distance along the x-axis for one complete cycle of the wave. It is calculated as \( \frac{2\pi}{|B|} \) where B is the coefficient of x.
6.
FLASHCARD QUESTION
Front
What is the phase shift in the function y = 2 sin(3x - \frac{\pi}{2})?
Back
The phase shift is calculated as \( \frac{-C}{B} \). Here, C = -\frac{\pi}{2} and B = 3, so the phase shift is \( \frac{\frac{\pi}{2}}{3} = \frac{\pi}{6} \) to the right.
7.
FLASHCARD QUESTION
Front
What does a negative amplitude indicate in a sine or cosine function?
Back
A negative amplitude indicates that the graph is reflected over the midline, but the amplitude itself is still considered positive.
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