# How do you graph y=2sin(x + pi)?

Apr 15, 2016

#### Explanation:

A typical graph of $y = \sin x$ has domain for all values of $x$ and range is from $\left[- 1 , 1\right]$.

It is a cyclical curve and repeats after every $2 \pi$, hence its period is $2 \pi$.

It's value is $0$ at each $n \pi$, it touches a maximum value of $1$ at each $2 n \pi + \frac{\pi}{2}$ and a minimum value of $- 1$ at each $2 n \pi - \frac{\pi}{2}$ (where $n$ is an integer).

It appears like graph{sin(x) [-10, 10, -2, 2]}

If we draw the graph of $y = 2 \sin \left(x + \pi\right)$, the range will be doubled due to multiplier $2$ and will be $\left[- 2 , 2\right]$.

However, the graph will be shifted by $\pi$ and hence minimum value will be $- 2$ at each $2 n \pi + \frac{\pi}{2}$ and a maximum value of $- 2$ at each $2 n \pi - \frac{\pi}{2}$ (where $n$ is an integer). But the function will continue to have value $0$ at each $n \pi$.

As the period of curve is $2 \pi$, it does not matter whether you say it has shifted by $\pi$ to the left or right.

The graph of $2 \sin \left(x + \pi\right)$ appears like graph{2sin(x+pi) [-10, 10, -2, 2]}