Simplify \({14}^{2}\) to \(196\).
\[196={10}^{2}\times {5}^{2}-2\times 10\times 5\cos{x}\]
Simplify \({10}^{2}\) to \(100\).
\[196=100\times {5}^{2}-2\times 10\times 5\cos{x}\]
Simplify \({5}^{2}\) to \(25\).
\[196=100\times 25-2\times 10\times 5\cos{x}\]
Simplify \(100\times 25\) to \(2500\).
\[196=2500-2\times 10\times 5\cos{x}\]
Simplify \(2\times 10\times 5\cos{x}\) to \(100\cos{x}\).
\[196=2500-100\cos{x}\]
Subtract \(2500\) from both sides.
\[196-2500=-100\cos{x}\]
Simplify \(196-2500\) to \(-2304\).
\[-2304=-100\cos{x}\]
Divide both sides by \(-100\).
\[\frac{-2304}{-100}=\cos{x}\]
Two negatives make a positive.
\[\frac{2304}{100}=\cos{x}\]
Simplify \(\frac{2304}{100}\) to \(\frac{576}{25}\).
\[\frac{576}{25}=\cos{x}\]
Switch sides.
\[\cos{x}=\frac{576}{25}\]
Ask: What values of \(x\) will make \(\cos{x}\) equal \(\frac{576}{25}\)?
\[x=\cos^{-1}{(\frac{576}{25})},2\pi -\cos^{-1}{(\frac{576}{25})}\]
Since cos is a periodic function, add the periodicity.
\[\begin{aligned}&x=2\pi n+\cos^{-1}{(\frac{576}{25})},n \in Z\\&x=2\pi n+2\pi -\cos^{-1}{(\frac{576}{25})},n \in Z\end{aligned}\]
x=sequence(2*PI*n+arccos(576/25),in(n,Z)),sequence(2*PI*n+2*PI-arccos(576/25),in(n,Z))
