SOLUTION: Given the function, y=1/2 sin (x/4+2pi)-3, identify the period and the phase shift.

Algebra ->  Trigonometry-basics -> SOLUTION: Given the function, y=1/2 sin (x/4+2pi)-3, identify the period and the phase shift.       Log On


   



Question 967368: Given the function, y=1/2 sin (x/4+2pi)-3, identify the period and the phase shift.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=%281%2F2%29sin%28x%2F4%2B2pi%29-3
A periodic function is a function, such as sin(x), that repeats its values in regular intervals
Sin(x) oscillates, or goes back and forth, between its maximum and minimum value.
The amplitude of the graph is the maximum height the graph reaches from the x-axis.
The period is the distance along the x-axis that is required for the function to make one full oscillation.
The phase shift is the measure of how far the graph has shifted horizontally.
Equation for graphing cos function:
y=Asin%28Bx-C%29%2BD
For given function:
y=%281%2F2%29sin%28x%2F4%2B2pi%29-3
Amplitude: A (absolute value)
A=1%2F2
Period: %282pi%29%2FB
B=1%2F4
Period=2pi%2FB=2pi%2F%281%2F4%29=8pi => periodic in x with period 8pi
Phase Shift: -C%2FB=-2pi%2F%281%2F4%29=-8pi
Vertical Shift (up or down): D=-3=> (3 units down)

+graph%28+600%2C600%2C+-55%2C55%2C+-10%2C+10%2C%281%2F2%29sin%28x%2F4%2B2pi%29-3%29+