phase shift?

Question

amplitude=2
period=pi
phase shift=1/8pi
vertical shift=4

i've gotten it down to these two choices but i don't understand the phase shift part

a. y= +-2sin(1/2x-4pi)+4
b. y= +-2sin91/2x-1/4pi)+4

Answer 1

y = (a)sin[b(x - c)] + d

a is amplitude.
b is 2[pi] / period
c is phase shift.
d is vertical shift.

plug them in and get y = 2sin(2x -1/4[pi]) + 4

Answer 2

You need to find the value of B (2л/period) and then we can create the part of the equation that includes phase shift. B = 2л/л = 2. So you put B outside the parentheses that contains the phase shift:

2(x-л/8) OR (2x - л/4) if the answer choice shows the B distributed into the parentheses. But remember, if you are creating your own equation from the given information, do B(x-h) first and then distribute if you must. "h" is the phase shift in that example.

Answer 3

y = 2.sin (2x - π/8) + 4
This equation has:-
Amplitude 2
Period π
Phase shift π/8
Vertical shift 4

Answer 4

y = k*sin(2πx/p + Φ) + s
k = amplitude
p = period
Φ = phase shift
s = vertical shift
x = independent variable (usually time, but not always ☺)

So (in your problem)
y = 2*sin(2x + π/8) + 4

The 'phase shift' refers to translation (shifting) along the x axis.

HTH

Doug