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

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See below.

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**Problem:**

How do you graph and list

a) the amplitude,

b) period,

c) phase shift

for

**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 # 2pi #**

**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.**

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