Question

If we know one trigonometric function (sin, for example), can we calculate the others?

Answer 1

We kind of also need to know which quadrant it is on, but, probably, yes...

Answer 2

I mean, for example, we could know that
tan x = 1, however, all this tells us about the sin of the function is that
\[\Large \sin(x) =\frac{\sqrt2}{2} \qquad \color{red}{or} \qquad\sin(x) = -\frac{\sqrt2}{2} \]

However, if we knew that x is in the first quadrant, then naturally, only the first is true.

^_^