College Algebra & Trigonometry, 2018a

9.3. THE VERTICAL SHIFT OF A TRIGONOMETRIC FUNCTION 411
9.3 The Vertical Shift of a Trigonometric Function
If a constant is added or subtracted to a trigonometric function, this will affect
the y-values of the function. If we consider the function y =5+sinx, then each
of the standard y-values would have 5 added to it, which would shift the graph
up 5 units.
The chart below considers just the quadrantal values for the sine function:
θ sin θ 5+sinθ
0 0 5
π/2 1 6
π 0 5
3π/2 −1 4
2π 0 5
7
6
y =5+sinx
5
4
3
2
1
y =sinx
−1
0
π
2
π
3π
2
2π
−2