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

Why when graphing a regular tan graph, the period is pi but when I graph a sin or cos it has a period of 2pi?

- PreCalc -
**Steve**, Wednesday, December 19, 2012 at 5:16pm
sin 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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