BQ#2: Unit T Intro-How do the trig graphs relate to the Unit Circle?

Terms to help for the reading below:

         PERIOD-graphs are cyclical and once completion of one cycle its called a period.

         AMPLITUDES-are half the distance between the highest and lowest points on the graph.

Photo-credit: Fabulous and Beautiful Victoria Ventura

Photo-credit: Fabulous and Beautiful Victoria Ventura

A. Period?-Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi? Interesting question. As seen from the lovely drawn pictures from above, we notice that both in sine and cosine we have repeating patterns: +,+,-,- and +, -, -,+. In order to complete a period we must go all around the unit circle. Keep in mind our graphs are just the unit circle unfolded and repeated with the same period. From 0 degrees to 360 degrees is 2pi. So that is why sine and cosine are 2pi. Seen from the picture below, we see that the pattern is +,-,+,-. The reason why tangent and cotangent's period is only pi is because the pattern is already completed by pi, unlike sine and cosine, in which one has to go all around in order to complete the period. Life is much easier doing tangent and cotangent, to be honest. 

Photo-credit: Fabulous and Beautiful Victoria Ventura

B. 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? In the Unit Circle all the other trig functions could be greater than one (YAY, for them) but for sine and cosine, they couldn't be greater than one. Which makes complete sense why the amplitude for sine and cosine is restricted to one and the others CAN be greater than one (such rebels.)


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