# How do you graph y=-2sinpix and include two full periods?

May 18, 2018

See the explanation:

#### Explanation:

First, find the amplitude and the period and phase shifting:

$a \sin b x + c$
amplitude: $| a |$
period: for sine its period is $2 \pi$ so $\frac{2 \pi}{b}$
phase shift: $- c$

So

amplitude = $| - 2 | = 2$

period = $\frac{2 \pi}{\pi} = 2$

fourth period: $\frac{2}{4} = \frac{1}{2}$

phase shifting = no phase shifting.((starts at 0)) origin

for myself to graph $\sin$ or $\cos$ I use a method that I take fouth the period and add it to the phase shift to go to the right and to the left by subtracting

"""one thing you have to keep in your mind which is the standard graph of $\sin$"""

$- 2 \sin \pi x$

it is negative so it starts at the origin and goes down if it is positive it will go up

so first point you plot at the origin then move fourth period to the right by adding $0 + \frac{1}{2}$

first point at the origin
$\left(0 , 0\right)$

to the right:

$\left(\frac{1}{2} , - 2\right)$ go down

$\left(1 , 0\right)$ back to average

$\left(\frac{3}{2} , 2\right)$go up

$\left(2 , 0\right)$back to average

"this is a full period"

to the left by back to the origin and subtract fourth period:
$\left(0 , 0\right)$ at average

$\left(- \frac{1}{2} , 2\right)$ go up

$\left(- 1 , 0\right)$ back to average

$\left(- \frac{3}{2} , - 2\right)$ go down

$\left(- 2 , 0\right)$ back to average

plot and connect the points

these are two full periods a period at the right of the y-axis and a period to the left of the y-axis you could make them both at the right or both at the left.

graph{-2*sin(pix) [-4.93, 4.935, -2.113, 2.82]}