Write trig function given features

Question

Write a sine function that has a midline of 3, an amplitude of 2 and a period of 7pi/6

Answer 1

The most difficult part of this is figuring out the B value for the equation.

2π/B = period

2π/B = 7π/6 Cross multiply

12π=7πB Divide by 7π and reduce

12π/7π=7π/7πB

B=12/7

y = 2 sin (12/7x) + 3