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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.)

**continue scrolling**

## Cosine

**continue scrolling**

**here we go, but continue scrolling just in case**

## Tangent/Cotangent

Meanwhile with tangent and cotangent.....

Just remember again to keep in mind that a period is one time through their cycle, their pattern.

**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.

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