# Need help solving an unknown

#### mortalcyrax

I am having trouble solving for x in this equation

$$\displaystyle 0=10sin(1.256637061*3+x)$$

If someone could help, it would be greatly appreciated.

#### Anonymous1

I am having trouble solving for x in this equation

$$\displaystyle 0=10sin(1.256637061*3+x)$$

If someone could help, it would be greatly appreciated.
You could simply argue that $$\displaystyle \sin(0) = 0.$$

$$\displaystyle 0=10\times\sin(\underbrace{1.26\cdot3+x})$$ Set this part equal to 0 and solve.

Or,

$$\displaystyle 0=10\times\sin(1.26\cdot 3+x)$$

$$\displaystyle \implies \sin(3.77+x) =0$$

$$\displaystyle \implies \sin^{-1}(\sin(3.77+x)) =\sin^{-1}(0)$$

$$\displaystyle \implies 3.77+x =0$$

$$\displaystyle \implies \fbox{x= -3.77}$$

mortalcyrax

#### Anonymous1

Note that their are infinitely many solutions to this equations since

$$\displaystyle \forall$$ $$\displaystyle n \in \mathbb{Z}$$

$$\displaystyle \sin(n\cdot \pi) = 0$$

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So the final solution will be: $$\displaystyle 1.256637061*3+x = k\pi$$ where k belongs to Z. Hence, $$\displaystyle x=k\pi-1.256637061*3$$