BQ#2: Unit T Concept Intro: Trig Graphs and the Unit Circle

How do trig graphs relate to the Unit Circle?
   Okay so I know what you are thinking..the Unit Circle again?! Well yes, the Unit Circle comes in from everywhere and somehow has a function for everything. For trig graphs, it is as if you are seeing the Unit Circle, yet in a straight line and the same numbers are present in order. Also, their signs depend on what quadrant they are found in. For example, if we have cosine, we know that it is positive in quadrants 1 and 4.

1. Period? Why is the period for sine and cosine 2pi, whereas the period for the period for tangent and cotangent is pi?
    The period for sine and cosine is 2pi due to the pattern that it follows and how it repeats after every four marks on a graph. Now, for tangent and cotangent and we are able to see that it repeats every two marks. For proof we can see it after knowing that the symbols are positive, negative, positive, negative and so that means that it only takes two marks. 

2. Amplitude?-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?
    So first of all, what are amplitudes? Well an amplitude is half the distance between the highest and lowest points on the graph. They can be found by looking at the value of |a|. Sine and cosine have the same amplitude of which is 1 and -1 due to the fact that they are the ones with the restrictions. They cannot be any points greater than or less than 1 and -1 since they don't exist anymore. Now, we get to tangent and cotangent. They have no restrictions and therefore can keep going on and on and on. Their range will always be negative infinity to positive infinity. Lastly, we have cosecant and secant of which simply don't have a range and therefore no amplitudes.