The trig functions when graphed relate to the unit circle because when their values graphed and on the unit circle are the same there simple extended when there graphed.
Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
It takes up to all four quadrants to repeat the same pattern. tangent and cotangent have a period of pi because they already have a positive and negative value on the first two quadrants.
Sine and cosine can not be bigger than one because of their ratios.