Need help solving an unknown

Apr 2010
16
0
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.
 
Nov 2009
517
130
Big Red, NY
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,

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

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

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

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

\(\displaystyle \implies \fbox{x= -3.77}\)
 
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Nov 2009
517
130
Big Red, NY
Note that their are infinitely many solutions to this equations since

\(\displaystyle \forall\) \(\displaystyle n \in \mathbb{Z}\)

\(\displaystyle \sin(n\cdot \pi) = 0\)
 
Last edited:
Feb 2010
100
27
Lebanon - Beirut
So the final solution will be: \(\displaystyle 1.256637061*3+x = k\pi\) where k belongs to Z. Hence, \(\displaystyle x=k\pi-1.256637061*3\)