It looks like you have an equation involving the cosine function: \(\cos(x) = 0.1\). To solve for \(x\), you need to find the angle whose cosine is 0.1. This can be done using the inverse cosine function, often denoted as \(\cos^{-1}\) or \(\arccos\).

\[ x = \arccos(0.1) \]

The \(\arccos\) function will give you the principal value of \(x\) in the range \([0, \pi]\) (or \([0^\circ, 180^\circ]\) if you are working in degrees).

Using a calculator:

\[ x \approx \arccos(0.1) \approx 1.4706 \text{ radians} \]

or in degrees:

\[ x \approx \arccos(0.1) \approx 84.26^\circ \]

However, the cosine function is periodic with a period of \(2\pi\) radians (or 360 degrees), and it is symmetric about \(x = \pi\). Therefore, the general solutions for \(x\) can be written as:

\[ x = 2k\pi \pm \arccos(0.1) \]

where \(k\) is any integer.

So, the complete set of solutions in radians is:

\[ x = 2k\pi + 1.4706 \]
\[ x = 2k\pi - 1.4706 \]

And in degrees:

\[ x = 360k + 84.26^\circ \]
\[ x = 360k - 84.26^\circ \]

where \(k\) is any integer.