BQ#2- Unit T Concept Intro

How do the trig graphs relate to the unit circle?

The trig graphs are just the unit circle unraveled. If you were to take the circle and stretch it into a line then you get your four quadrants but just in a straight line. In the unit circle each quadrant angle could be turned into radians, the first quadrant would be pi/2, the second quadrant would be pi, the third quadrant would be 3pi/2, and the fourth quadrant would be 2pi. For sine the pattern would go POSITIVE for the first two quadrants and NEGATIVE for the last two quadrants. In cosine the pattern is POSITIVE, NEGATIVE, NEGATIVE, POSITIVE. Finally for tangent it will start of with POSITIVE,NEGATIVE, POSITIVE, and NEGATIVE. as you see the "All Students Take Calculus" also applies to the graphs. 

Period?-  why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?

The period for sine and cosine is 2pi because unlike tangent and cotangent the pattern for sine and cosine does not repeat until the second time around the "unit circle". The patterns aren't repeated which means that for a full period it has to reach 2pi. For tangent and cotangent it's period is only pi because it's pattern is repeated (positive,negative,positive,negative) which means that there is no need to reach 2pi because it would be exactly the same. 

Amplitude?- how does the fact that sine and cosine have amplitudes of one (and ogre trig functions don't have amplitudes) relates to what we know about the unit circle?

Sine and cosine both have the ratio of having "r" as the denominator. Cosine's ratio being x/r and sine being y/r, in the unit circle "r" always equals one since it is the radius of the unit circle.  With that you realize that the boundaries for sine and cosine is between 1 and -1. Now for tangent it's different because the ratio for tangent is y/x and the x can be multiple values not only 1 and -1 which means it has no restrictions.