Can someone provide me with a visual proof (unit circle) that tanx=sinx/cosx?
In fact, tan(x) = sin(x)/cos(x) is often taken to be the definition. Do you need a proof that tan(x) is the length of the tangent to the unit circle, as the orange segment in the following picture (taken from the TikZ manual)?
This is because the two triangles are similar, so tan(α)/sin(α) = 1/cos(α).