1. Are the graphs of y = sin x and y = 2sin x the same shape?

Yes, they are the same shape. However they have different amplitudes. y = 2sin x is a "stretched out" version of y = sin x

2. Is the graph of y = sin x the same as the graph of y = cos(x + π)?

Yes, the graph of second function is a translation of y = sin x of 180° and thus the two graphs are the same.

3. Can the sine of an angle greater than 360o be found?

Yes, the sine, cosine and tangent of any sized angle can be found (even negative ones).

The functions are called periodic functions and exist for all angles. On most occasions graphs are drawn between 0o and 360o.