# Solving sin(x) = 0

#### tony77

##### New Member
The problem with the problem im trying to solve is that I dont understand what to do. The problem goes as follows: "use the appropriate extended graph to find all values of x in the interval [-2pi, 2pi] that satisfy the equation: sin x = 0"

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#### MarkFL

##### La Villa Strangiato
Staff member
Moderator
Math Helper
Here's a graph of the given function over the stated domain, with the solutions shown:

In general, the equation:

$$\displaystyle \sin(x)=0$$

Implies:

$$\displaystyle x=k\pi$$ where $$k\in\mathbb{Z}$$

We are told:

$$\displaystyle -2\pi\le x\le2\pi$$

Hence:

$$\displaystyle -2\pi\le k\pi\le2\pi$$

$$\displaystyle -2\le k\le2$$

And so:

$$\displaystyle k\in\{-2,-1,0,1,2\}$$

which means:

$$\displaystyle x\in\{-2\pi,-\pi,0,\pi,2\pi\}$$

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