Question

A sine function has a phase shift of 60° to the right and a vertical translation of 2 units down. What is a possible equation for this function?

a) y = sin(x - 60°) - 2
b) y = sin(x + 60°) - 2
c) y = sin(x - 60°) + 2
d) y = sin(x + 60°) + 2

Answer 1

The equation for a sine function with a phase shift of 60° to the right and a vertical translation of 2 units down is y = sin(x - 60°) - 2.

Step-by-step explanation:

The equation for a sine function with a phase shift of 60° to the right and a vertical translation of 2 units down is y = sin(x - 60°) - 2.

A phase shift affects the horizontal position of the graph, so when it is positive, as in this case, it results in a shift to the right. The vertical translation of 2 units down means the entire graph is shifted downward by 2 units.