a. The period for sine and cosine is 2pi because thats is howl long it takes for the pattern to repeat. By pattern I mean for the positive and negative quadrant patterns. We know that a trig graph of sine is ++-- this means that the first to quadrants of the graph will be above the X axis and the othe will be under. Tangent /Cotangent however, will be pi because you only need one section for the pattern to repeat. The pattern for tangent/cotangent is +-+- however you only need +- because the pattern repeats already.
b. Sine and cosine have restrictions because the unit curcle is only goes up to. 1, -1, 0. For the same reason sine and cosine can only equal >-1 & <1. To quote Mrs. Kirch, " Sine and Cosine cannot bust through the restrictions."
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