# Thread: Need help solving an unknown

1. ## Need help solving an unknown

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.

2. Originally Posted by 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.
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,

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

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

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

$\displaystyle \implies 3.77+x =0$

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

3. Note that their are infinitely many solutions to this equations since

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

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

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