Positive cosine is first or fourth quadrant. So we don't know the sign of the sine or the tangent.
Everybody's favorite right triangle is 3/4/5 and here we have
[tex]\left(\dfrac 3 5 \right)^2 + \left(\dfrac 4 5 \right)^2 = 1[/tex]
So if
[tex]\cos \alpha = 0.6 = \dfrac 3 5[/tex]
then
[tex]\sin \alpha = \pm \dfrac{4}{5} = \pm 0.8[/tex]
and
[tex]\tan \alpha = \dfrac{\sin \alpha}{\cos \alpha} = \dfrac{\pm 0.8}{0.6}=\pm \dfrac 4 3[/tex]
