Solving sin(x) = 0

tony77

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Apr 15, 2019
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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

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Jan 25, 2018
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Here's a graph of the given function over the stated domain, with the solutions shown:

tml_0001.png


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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