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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 -

    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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