Unit 5 – Day 2: Midline and Amplitude
I.
Name: KEY
Graphing Form of Trig Functions
a. The graphing form of a trig function (for example cosine) is
y = a cos(x-h) + k
II.
Midline
a. The midline is the line that “cuts the graph in half.”
b. The midline is halfway between the max and min
c. The midline can be found using the following formula:
Midline is at y = k or y =
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!
d. When there is no vertical shift, the midline is always y = 0.
III. Amplitude
a. The amplitude describes the distance from the midline to the max or
min.
b. The amplitude of the standard sine and cosine graph is 1.
c. The amplitude of a sine or cosine graph can be found using the
following formula:
Amplitude = |𝑎| Or !
IV.
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!
!
Find the amplitude and midline for each of the following:
1. y = 3sinx
Amplitude: 3
Midline: y = 0
Amplitude: 4
Midline: y = -1
Amplitude: 1/3
Midline: y = 5
2. y = -4cos(x + 90) - 1
3. y = (1/3)sinx + 5