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August 23, 2014

August 23, 2014

Posted by **Skye** on Wednesday, December 19, 2012 at 5:08pm.

- PreCalc -
**Steve**, Wednesday, December 19, 2012 at 5:16pmsin and cos change smoothly from 0 to 1, then 0 to -1 and back every 2pi

tan varies from 0 to infinity, flips over to minus infinity, and comes back to 0 after only pi.

tan(x+pi) = (tanx + tan pi)/(1-tanx*tanpi)

= (tanx + 0)/(1-0)

= tanx

so every pi tan comes back around. As the radius rotates around the 2pi unit circle, sin and cos make one period each. tan starts all over each time the slope is vertical, which happens twice during each 2pi period.

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