Question: The sine function has an amplitude of 2, a phase shift of π/6 to the right, a period of 8π, and a vertical translation of 2 units down. Write an equation for the function

Question

The function I've made is: y = 2sin (8π(x+π/6))-2

Is it accurately based on the guidelines in the question?

Answer 1

close, but no cigar
period of sin(kx) is 2π/k
so if the period is 8π,
2π/k = 8π
k = 1/4
f(x-h) shifts h to the right
y = 2 sin(1/4 (x-π/6)) - 2