a sine function has a maximum value of 4, minimum value of -2 and period of p. it passes through the point (p/3,1). what is the phase shift

Question

a sine function has a maximum value of 4, minimum value of -2 and period of π. it passes through the point (π/3,1). what is the phase shift

Answer 1

The function has the form y = Asin(Bx + C) + D

 

A is the amplitude, which is half the distance between the maximum and minimum values = 3.

 

D is the vertical shift:  The horizontal line y = 1 cuts the graph in half.  The line y = 1 is 1 unit above the x-axis.  So, D = 1

 

The period is 2π/B, so, since the period is π, we get 2π/B = π.              Therefore, B = 2.

 

So, y = 3sin[(2x + C)] + 1

 

We are also given that period = p   Thus, 2π/2 = p.  So p = π 

 

(p/3, 1) = (π/3, 1) is on the graph

 

Substitute into the equation to obtain:  1 = 3sin[2π/3 + C] + 1

 

   2π/3 + C = 0

 

                C = -2π/3

 

Phase shift = -C/B = (2π/3)/2 = π/3