1. The Unit Circle is a trig graph unraveled. It follows the same patterens as it does on the Unit Circle. When you have sine on the Unit Circle, it is going to be + + - -, on the trig graph it is the same thing it is up up then goes down down and that ends that period of the graph and on the Unit Circle it marks then end of a whole circle.
The period of sine and consine is 2pi because then you look at the negatives and positive from the Unit Circle, it takes one whole circle for the pattern of positives and negatives to start again. When you go around the Unit Circle completely that is 2 pi, that is why the period is 2pi. The reason why tangent and cotangent is pi is because it takes half the circle for the pattern to start over.
Sine and cosine are the only ones that have an amplitude, they are also the only two graphs that do not have that do not have asymptotes. All the other graphs have asymptotes because they certrain points where the graph is undefined and does not touch those points. With sine and cosine they graph will touch any points as long as they are within the amplitude. With all the other trig functions they have asymptotes. Amplitude and asymptotes are restrictions for each graph.
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