Tuesday, April 15, 2014

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

Sine and Cosine In these images you see how the Unit Circle translates and unravels itself into a sine curve graph. 

Period: The period for sine and cosine is 2pi because it takes four quadrants (ASTC) to repeat the pattern. Sine's pattern according to ASTC from the unit circle is + + - -

 While cosine's pattern is + - - +
It merely takes all of the unit circle (which is 2pi at 360* to complete sine and cosine's patterns.
Graphs are merely snapshot of the graph, these graphs are infinite as circles are - no ends, no beginning but for the sake of this class we will only be graphing one single period.

 Amplitude: Remember that sine equals y/r and cosine equals x/r and that r=1. In the unit circle, the values cannot be bigger or smaller than 1, thus x and y always equal 1. 1 divided by 1 equals *drumroll please* ONE!!!
Meanwhile all the other trig functions have asymptotes because they do not have "r" such as tangent and cotangent (y/x and x/y respectively.)

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Meanwhile with tangent and cotangent.....
Period: Tangent and cotangent have a period of just pi. According to ASTC from the Unit Circle, the pattern this trig function has is + - + -. Meaning the pattern is completed in the first two quadrants which is 180* aka pi aka half of the circle.
Just remember again to keep in mind that a period is one time through their cycle, their pattern. 

Images found here.

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