BQ #2: How do the Triq Graphs Relate to the United Circle?

A. Period? Why is the peirod for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?

A period is the end and beginning of a cycle. It ends and starts when there is a repeating patterns. In this case. the reason why sine and cosine is 2 pi is because the pattern repeat itself fully around the Unit CIrcle. For tangent/cotangent, the pattern repeats only half way. For example in quadrant 1, tangent is positive, qudrant II negative, qudrant III positive, and quadrant IV negative. Therefore, it repeat itself only half of the graph.

Below are the sign for the triq function. The patterns can be seen by looking at the sign from Qudrant I to Qudrant IV.

The graph below also demonstrates how the triq function of sine and cosine relates to the unit circle. It marks the period of a cycle of a pattern. It would take 2pi for sine and cosine to repeat.

B. How does the fact that sine and cosine have amplitudes of one (and the other triq functions don't have amplitudes) relate to what we know about the Unit Circle?

IT relates to what we  know about the Unit Circle because sine is between 1 and -1 while cosine is between -1 and 1. Therefore, there is no restriction for the other triq function.

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