The graph of a sine function g(x) is presented below.
Part A: Explain how to determine the value of the vertical translation, d, for the graph of g(x).
Part B: Explain how to determine the value of the vertical translation, d, for the graph of f(x) = 9sin(θ + 60°) + 6.
Part A: Up 9
Part B: Up 6
Part A: The graph appears to be a cosine graph since it starts at a peak on the y-axis. Normally a cosine graph starts at (0,1). This graph begins at (0,10). It has been shifted up y a translation by 9.
Part B: Each trig equation has a basic structure f(x) = a sin (x+b) + k where:
= a is the vertical stretch
= b is the horizontal shift
= k is the vertical shift
A vertical translation is a vertical shift and is represented by the value in k added outside of the function. In the equation f(x) = 2sin(θ + 120°) + 6, k = 6. The vertical translation is 6.