Question

Let α and β be the angles made be A and -A with the positive X-axis. Show that Tanα = Tanβ. Thus, giving Tanθ does not uniquely determine the direction of A.

Answer 1

If a vector A makes α with x-axis then -A makes an angle (π+α) = β with same positive direction of x-axis ==> Tanβ = Tan(π+α) = Tanα……..QED

So yes if we only give Tanθ of a vector where θ is the angle made by the x-axis, it doesn’t uniquely determine the direction of a vector.