# How do you graph and list the amplitude, period, phase shift for y=-1/2sinx?

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Nimo N. Share
Feb 9, 2018

See below.

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Problem:
How do you graph and list
a) the amplitude,
b) period,
c) phase shift
for  y = −1/2 sin(x)  ?

a) the amplitude
The amplitude of the sine function is defined as 1/2 the distance between its maximum and minimum values.

The amplitude of sin(x) is 1.
In the given function, each value of sin(x) is multiplied by (-1/2). so it is only 1/2 the distance from the x-axis, which means
the amplitude of the given function is 1/2.

b) period
The period is exactly the same as for sin(x).
The period of the given function is $2 \pi$

c) phase shift
The sign of the given function is negative for every value of x where sin(x) is positive, and vise versa, and it passes through zero for the same values of x, The phase shift could be expressed in one of two ways:

One can say either that the phase shift is $+ \pi$, or that the phase shift is $- \pi$, and the graph would look the same.

$y = \sin \left(x\right)$

$y = - \frac{1}{2} \cdot \sin \left(x\right)$

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