Is y equal to cotx, tanx, cosx, or sinx if its graph is periodic with a period of 2pi, an amplitude equal to 1, and it passes through the origin?

Answer 1

Plot the graphs. It is equal to sin(x).
Proof: cot(x), tan(x) have period pi and no amplitude in the classical way.
cos(0)=1, hence it cannot pass through the origin, whereas sin(0) = 0, yielding sin(x) to be the function-in-question.

Answer 2

thanks.