Question

What are the values of sin α and tan α, if:
cosα=0.6

Answer 1

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

$\left(\dfrac 3 5 \right)^2 + \left(\dfrac 4 5 \right)^2 = 1$

So if

$\cos \alpha = 0.6 = \dfrac 3 5$

then

$\sin \alpha = \pm \dfrac{4}{5} = \pm 0.8$

and

$\tan \alpha = \dfrac{\sin \alpha}{\cos \alpha} = \dfrac{\pm 0.8}{0.6}=\pm \dfrac 4 3$