Unit T Big Question #1

a. Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?
          Considering each mark in the graphs above equal pi/2........we see that since sine and cosine's pattern continues on throughout the entire 2pi without repeating, we know that they need 2pi to be able to represent a "snapshot" of the actual graph. On the other hand, tangent and cotangent only need up to pi for them to successfully show a part of their graphs.

b. How does the fact that sine and cosine have amplitudes of one (and the other trig functions don't have amplitudes  relate to what we know about the Unit Circle?
          Taking in mind the sine graph, we see that the amplitude is 1, this is because the sine of 0 is 0, while the sine of 90 is 1 and the sine of 270 is -1 and the sine of 360 is also 0. For cosine graphs, we see that the cosine of 0 is 1, while the cosine for 90 is 0 and the cosine for 180 is -1 and the cosine for 360 is 1. The reason that these graphs have amplitudes is because there are high and low points as described in the definition of an amplitude: "Amplitudes are half the distance between the highest and lowest point on the graph" (WSQ).