# How do you graph #g(x) = -2sin(pix+pi/3)#?

##### 1 Answer

#### Answer:

There are several steps.

#### Explanation:

(or, in some treatments

We know that sine takes on values between

The amplitude reflects this fact and is equal to

For the basic sine graph,

The period of

Phase shift (or Horizontal Shift) tells us where we "start the first period" it tells us when we take the sine of 0.

To find the shift, solve

(Or

So here we go:

For

We have Amplitude =

(The minus sign will flip the graph across the

Period is

Phase Shift is the solution to

it is

#-1/3#

The graph starts on the

Here is one period:

graph{y = -2sin(pix+pi/3) *(sqrt(1-(x-2/3)^2))/(sqrt(1-(x-2/3)^2)) [-4.177, 5.69, -2.59, 2.343]

**Note**

Another way of finding the period is to find the beginning of the first cycle (phase shift) by solving

The period is the difference between the end and the beginning. If you go through the algebra, you'll see that the difference is