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Thread: Finding the two possible values of an angle

  1. #1
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    Finding the two possible values of an angle

    Hi,

    I was asked to find the two possible values of (TanA = -2/6), but I'm having some trouble here. In my text, it says the related acute angle is the angle between the terminal arm and the closest part of the x-axis. That would lead me to believe that if the acute angle is 18.43 degrees, then the angle in quadrant II would be 180 - 18.43 = 161.57. And in quadrant IV, 360 - 18.43 = 341.57.

    This doesn't seem right to me. When I plot it on a grid, the acute angle in quadrant II is 18.43 degrees from the y-axis. In this case the angle would be 108.43 degrees. My lesson text wasn't very clear on this and I don't have any way of communicating with a teacher. I would greatly appreciate any help and clarification.

    Finding the two possible values of an angle-math-work.jpg

    Here's my written work, I apologize for the sloppiness.

    Thanks again.
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  2. #2
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    Re: Finding the two possible values of an angle

    Hey jpompey.

    I'd suggest you trying to check your answer independently with a calculator or computer program so that you can independently verify it yourself.
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  3. #3
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    Re: Finding the two possible values of an angle

    Finding the two possible values of an angle-clipboard01.jpg

    $\theta$ are the two angles $-\pi < \theta \leq \pi$ that will have $\tan(\theta) = \dfrac{-2}{6}$

    remember that $\dfrac{-2}{6} = \dfrac{2}{-6}$

    They happen to be $\theta = -18.435^\circ,~~\theta = -18.435^\circ + 180^\circ = 161.565^\circ$
    Thanks from jpompey and HallsofIvy
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  4. #4
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    Re: Finding the two possible values of an angle

    Thank you very much, that completely escaped my mind. I appreciate your help.
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  5. #5
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    Re: Finding the two possible values of an angle

    What a proper solution of the question! Thanks for being so sincere with us!
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