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Thread: What is cot(x)=0

  1. #1
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    What is cot(x)=0

    Can cot(x)=0 and what are the values.

    And also, how would I solve this.
    $\displaystyle cot^2x-cotx=0$
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Can cot(x)=0 and what are the values.

    And also, how would I solve this.
    $\displaystyle cot^2x-cotx=0$

    $\displaystyle \cot(x)=\frac{\cos(x)}{\sin(x)}$

    so it has the same zero's as the cosine function

    $\displaystyle \cot^2x-\cot(x) =0 \iff \cot(x) [\cot(x)-1]=0$

    so $\displaystyle \cot(x) = 0$ or $\displaystyle \cot(x)=1$

    $\displaystyle x=\pi \cdot k \mbox{ } k \in \mathbb{Z}$ and for the 2nd

    $\displaystyle x=\frac{\pi}{4}+\pi \cdot k \mbox{ } k \in \mathbb{Z} $
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