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How many answers does the equation $\sin{x}+\lfloor{\sin{x}}\rfloor=\frac{x}{3}+\lfloor{\frac{x}{3}}\rfloor$have(using gragh)?

Please help me I am stuck in drawing $\sin{x}+\lfloor{\sin{x}}\rfloor$and $\frac{x}{3}+\lfloor{\frac{x}{3}}\rfloor$ an dfind their intersections how should I work?

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    take a look here: http://www.wolframalpha.com/input/?i=plot+%7Bfloor(sin+x)%2Bsin(x),x%2F3%2Bfloor(x%2F3)%7D+for+x%3D-10+to+10 – 2017-01-09
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    @Math-fun How should we count the intersections by hand drawing? – 2017-01-09
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    when drawing by hand then you should be very careful, then yo ucould see all the intersections. – 2017-01-09

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The graph of $$ \sin x+ \lfloor \sin x \rfloor = \frac {x}{3} + \lfloor \frac {x}{3} \rfloor $$ is as follows (the red curves are for $\sin x +\lfloor \sin x \rfloor $ and the blue lines for $\frac {x}{3} +\lfloor \frac {x}{3} \rfloor $) :

enter image description here

If you want the intersection points,

enter image description here

Hope it helps.

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    $(0,-1)$ is not a solution. both functions are "void" at this point :-) – 2017-01-09
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    @Math-fun That's why I said intersection points while describing the second graph. – 2017-01-09
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    maybe I don't see your point, but the functions do not intersent at this point. – 2017-01-09