Use tan-1, which is atan on the calculator.
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{4}}}{{\mathtt{5}}}}\right)} = {\mathtt{38.659\: \!808\: \!254\: \!09^{\circ}}}$$
This is the first quadrant solution. There is also a third quadrant solution obtained by adding 180° to this.
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{38.659\: \!808\: \!254\: \!09}}^\circ\right)} = {\frac{{\mathtt{4}}}{{\mathtt{5}}}} = {\mathtt{0.8}}$$
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{180}}{\mathtt{\,\small\textbf+\,}}{\mathtt{38.659\: \!808\: \!254\: \!09}}\right)} = {\frac{{\mathtt{4}}}{{\mathtt{5}}}} = {\mathtt{0.8}}$$
.
Use tan-1, which is atan on the calculator.
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{4}}}{{\mathtt{5}}}}\right)} = {\mathtt{38.659\: \!808\: \!254\: \!09^{\circ}}}$$
This is the first quadrant solution. There is also a third quadrant solution obtained by adding 180° to this.
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{38.659\: \!808\: \!254\: \!09}}^\circ\right)} = {\frac{{\mathtt{4}}}{{\mathtt{5}}}} = {\mathtt{0.8}}$$
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{180}}{\mathtt{\,\small\textbf+\,}}{\mathtt{38.659\: \!808\: \!254\: \!09}}\right)} = {\frac{{\mathtt{4}}}{{\mathtt{5}}}} = {\mathtt{0.8}}$$
.