Equations PLEASE HELP

Question

Write an equation for the function that is described by the given characteristics.

A sine curve with a period of   , an amplitude of 4, a left phase shift of    , and a vertical translation down 5 units.

 

y= _______________________

Answer 1

Here's what you need to know. The transformations of the sine function are:

y = a·sin(b(x-c)) + d

where:

1. a is the amplitude = 4 in your problem
2. b is the horizontal (left/right) dilation = 2π/period. In your problem,period = 4π, so b = 2π/4π = 1/2
3. c = horizontal (aka phase) shift = -π/4 (negative since it's to the left)
4. d = vertical shift = -5 (negative since it's down)

Can you finish it?

Answer 2

y = Asin(Bx + C) + D;

Now A = 4, D = - 5; B = 2π/(4π) = 1/2; C/B = π/4, C = 1/2·π/4 = π/8.

So, y = 4sin(x/2 + π/8) - 5