BQ#2 – Unit T Concept Intro

*How do the trig graphs relate to the Unit Circle?

 Trigonometric graphs (dealing with sin,cos,tan, and their inverses) can easily be related to the Unit Circle. The graph actually in it of itself has trig graphs.

http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcirclegraphs.htm

http://www.regentsprep.org/Regents/math/algtrig/ATT5/unitcirclegraphs.htm

The following picture actually demonstrate  how a unit circle were to look if it were to be unwind. The way to know when a graph goes up or continues to go up or down it, it ties back with the saying "All Students Take Calc." For example, if we are dealing with sin, we know that sin is positive in the first and second quadrant, so then, like shown on the top left picture, the lines in quadrant 1 and 2 are positive and in 3 and 4, they are negative. 

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

 If you take a look at the picture shown on the left, if will help with understanding and my explanation to why the period for sine and cosine is 2pi when for tan and cot it is just pi. 

Well if you see the pattern of sin, ++--, and the pattern of cos, +-+-, you notice that that is the end of the pattern. So you know that ++- -or +-+- is the completion of 1 full round around  the unit circle which is also equivalent to 2pi, a whole round around the unit circle. However, with tan and cot it's different. Since there pattern is +-+- their full pattern basically ends at +- because then it starts over with +- again. With that being said, tan and cot only have periods of pi because there complete round, finishes at the pi mark and does not have to go around the unit circle completely.

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?

Amplitude determines how high a graph might go and how low it will go. A note to remember is that the same high it may have to go up, it will also be the same as that. So for example, is a graph an amplitude of 2 then the highest point on the graph will be 2 and the lowest point will be -2. However, for sine and cosine there amplitude will be 1 and -1 because the graph can only go up one and down one.