cos(x)=1/4

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} = {\mathtt{75.522\: \!487\: \!814\: \!07^{\circ}}}$$

x=75.52248781

Note that because cos(x) is also positive in the fourth quarter it could also be 

$${\mathtt{360}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)} = {\mathtt{284.477\: \!512\: \!185\: \!93}}$$

Check

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{284.477\: \!512\: \!185\: \!93}}^\circ\right)} = {\frac{{\mathtt{1}}}{{\mathtt{4}}}} = {\mathtt{0.25}}$$