e^(i t) = cos t + i sin t

How is the exponential function the same as sin function? I can't seem to picture it.. Does anyone have a graph of this function?

It's not the same. What gave you that idea? Also, the complex exponential is very difficult to "picture". You'd need a course on complex analysis to visualize what it's doing, but you only need basic calculus to derive this relationship.

Tailor expand e^(it), cos(t) and i sin(t). Then look at the results. Here are a couple concise proofs:
http://mathworld.wolfram.com/EulerFormula.html