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Math Help - Just need confirmation on a circular function question.

  1. #1
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    Just need confirmation on a circular function question.

    determine the value of the following if 0 is less than or equal to theta and theta is less than 2 pie.

    sec theta= -2root3/3= -root/3= 7pie/6
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  2. #2
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    Quote Originally Posted by Dave19 View Post
    determine the value of the following if 0 is less than or equal to theta and theta is less than 2 pie.

    sec theta= -2root3/3= -root/3= 7pie/6
    First, it's "pi" not "pie."

    Second, what exactly are you asking? These cannot all be equal to one another.

    Are you asking to find \theta when
    sec(\theta) = - \frac{2\sqrt{3}}{3}

    sec(\theta) = -\sqrt{3}

    and to find
    sec \left ( \frac{7 \pi}{6} \right )

    You've been asking for help on a large number of these. Why don't you tell us what you've been able to do so we can help you learn this better.

    -Dan
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  3. #3
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    heres what i have done.

    i will put it in steps 1,2,3,4


    sec theta= 1)-2root3/3 2) cos theta=1/sec theta 3) after the work it turns to -root3/2 4) then i have it as 7pie/6 and im unsure if there should be 5pie/6 in it to.
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Dave19 View Post
    i will put it in steps 1,2,3,4


    sec theta= 1)-2root3/3 2) cos theta=1/sec theta 3) after the work it turns to -root3/2 4) then i have it as 7pie/6 and im unsure if there should be 5pie/6 in it to.
    Okay, please in the future don't string those equal signs together like that. It is very confusing!

    sec(\theta) = -\frac{2\sqrt{3}}{3}

    cos(\theta) = -\frac{\sqrt{3}}{2}

    Now, this implies that we have a reference angle of \pi / 6. Cosine is negative in QII and QIII. So your solution will be
    \theta = \pi \pm \frac{\pi}{6}
    so your final solution is both 5\pi / 6 and 7 \pi / 6.

    -Dan
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