College Algebra & Trigonometry, 2018a

9.3. THE VERTICAL SHIFT OF A TRIGONOMETRIC FUNCTION 413
We have now examined three of the four transformations of trigonometric functions
that are discussed in this chapter - amplitude, period and vertical shift. A
general equation for a sinusoid that involves these three transformations would
be:
y = A sin(Bx)+D
or
y = A cos(Bx)+D
In determining an equation from a graph that involves a vertical shift, the value
of A will be half the distance between the maximum and minimum values:
A = max−min
2
and the value of D will be the average of the maximum and minimum values:
D = max+min
2
Example
Determine an equation that satisfies the given graph.
6
4
2
−2
0 3π
4
3π
2
9π
4
3π