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Thread: How to find the inverse tangent since the calculator is limited

  1. #1
    TWN
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    How to find the inverse tangent since the calculator is limited

    This is probably a basic concept that I just never really grasped...now I'm in Calc III and it's biting me in the butt.

    I need to find theta = arctan(-1/2)

    I typed it into my calculator to receive the answer -.464 radians

    But calculators are limited when it comes to solving trig, and as I understand there are other answers other than what I received. How do I go about finding the other answer(s)?
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  2. #2
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    Re: How to find the inverse tangent since the calculator is limited

    Quote Originally Posted by TWN View Post
    This is probably a basic concept that I just never really grasped...now I'm in Calc III and it's biting me in the butt.

    I need to find theta = arctan(-1/2)

    I typed it into my calculator to receive the answer -.464 radians

    But calculators are limited when it comes to solving trig, and as I understand there are other answers other than what I received. How do I go about finding the other answer(s)?
    This is equivalent to $\displaystyle \displaystyle \begin{align*} \tan{\theta} = -\frac{1}{2} \end{align*}$. The tangent function has a period of $\displaystyle \displaystyle \begin{align*} \pi \end{align*}$, so to get the general solution, you need to write $\displaystyle \displaystyle \begin{align*} + \pi n \end{align*}$ where $\displaystyle \displaystyle \begin{align*} n \in \mathbf{Z} \end{align*}$ after $\displaystyle \displaystyle \begin{align*} -0.464 \end{align*}$.
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  3. #3
    TWN
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    Re: How to find the inverse tangent since the calculator is limited

    Quote Originally Posted by Prove It View Post
    This is equivalent to $\displaystyle \displaystyle \begin{align*} \tan{\theta} = -\frac{1}{2} \end{align*}$. The tangent function has a period of $\displaystyle \displaystyle \begin{align*} \pi \end{align*}$, so to get the general solution, you need to write $\displaystyle \displaystyle \begin{align*} + \pi n \end{align*}$ where $\displaystyle \displaystyle \begin{align*} n \in \mathbf{Z} \end{align*}$ after $\displaystyle \displaystyle \begin{align*} -0.464 \end{align*}$.
    You started speaking a language I don't understand in the end there.
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  4. #4
    Kyo
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    Re: How to find the inverse tangent since the calculator is limited

    You can look up some math proof-symbols to find some of the common ones. What Prove It said there is: -0.464 + pi*n where n is an element of the real numbers.
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