Given Tan t = 1/2, How do you know that y=1 and x=2 and not the multiples of it?

Question

If sin t = 1 and cos t = 2 then tan t = 1/2 since tan = y/x

But this also works for sin t= 2 and cos t=4 because 2/4 = 1/2

So how do you know that x = 1and y = 2, not the multiples of it.

Answer 1

sint=2 and cost=4 are impossible. The maximum value for sine or cosine is 1, no matter what angle t is.

But if you mean how do you know the sides of a triangle are 1 and 2 and not some multiple, you don't know.

It could be any multiple, but not because sint=2 or cost=4.

If all you know are the tangent, sine, cosine or the angles, you have no information about the lengths of the sides All you know is their ratio.