Sinusoidal Functions Flashcards
What is the amplitude of a periodic function?
the vertical distance from the principal axis to the maximum
What is the period of a periodic function?
the horizontal length of one cycle
What is the principal axis of a periodic function?
A horizontal (flat) line around which the periodic function oscillates.
(a.k.a Midline)
Located halfway between the maximum and minimum.
ALWAYS WRITE IN THE FORM “y = ____”
How do you know the amplitude from an equation? y=asin(bx)+d
|a|
How do you find the period from an equation? y=asin(bx)+d
360/b
What is the amplitude in a ferris wheel problem?
The radius of the ferris wheel
What is the period in a ferris wheel problem?
the time it takes for one complete rotation
What is the principal axis in a ferris wheel problem?
The distance from the ground to the center axle of the ferris wheel.
How do you know the principal axis from an equation? y=asin(bx)+d
y=d
which type of sinusoidal function has a y-intercept at the principal axis?
y=sin(x)
or
y=cos(x)
y=sin(x)
which type of sinusoidal function has a y-intercept at the max or min?
y=sin(x)
or
y=cos(x)
y=cos(x)
How do you know if a is positive on a sine function?
on the y-axis, the graph starts at the principal axis and goes up to the maximum, then down to the minimum, and so on…
How do you know if a is negative on a sine function?
on the y-axis, the graph starts at the principal axis and goes down to the minimum, then up to the maximum, and so on…
How do you know if a is positive on a cosine function?
on the y-axis, the graph starts at the max, then goes down to the minimum, and so on…
How do you know if a is negative on a cosine function?
on the y-axis, the graph starts at the minimum, then goes up to the maximum, and so on…
How would you find the period of this graph?
Find the horizontal distance between the max and min, then multiply by 2
