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Math Help - numerical value (trig)

  1. #1
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    Thumbs down numerical value (trig)

    This chapter is so confusing to me. Is there a simple way to go about this?

    find a numerical value of one triganomic function of each x.

    2 sin^2x = 3 cos^2x

    1-sin^2x = 1/9

    1+ tan^2x = sin^2x + 1/sec^2x
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  2. #2
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    First one,
    2\sin^2x=3\cos^2x
    Use identity \cos^2x=1-\sin^2x.

    Thus,
    2\sin^2x=3(1-\sin^2x)
    Thus, open parantheses,
    2\sin^2x=3-3\sin^2x
    Thus,
    5\sin^2x=3
    Thus,
    \sin^2x=\frac{3}{5}=\frac{15}{25}
    Thus,
    \sin x=\pm\frac{\sqrt{15}}{5} \approx \pm.775
    Thus, all non-cotermial angles are, (use the arcsin)
    x\approx 51,129,231,309
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  3. #3
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    Second one,
    1-\sin^2x=\frac{1}{9}
    Use identity 1-\sin^2x=\cos^2x
    Thus, \cos^2x=\frac{1}{9}
    Thus,
    \cos x=\pm \frac{1}{3}
    Thus, all the non-coterminal angles, (use arccos)
    x\approx 71,109,251,289
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  4. #4
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    Problem 3,
    1+\tan^2x=\sin^2x+\frac{1}{\sec^2x}
    Use identity \frac{1}{\sec x}=\cos x
    Thus,
    1+\tan^2x=\sin^2x+\cos^2x
    Use identity \sin^2x+\cos^2x=1
    Thus,
    1+\tan^2x=1
    Thus,
    \tan^2x=0
    Thus,
    \tan x=0
    Thus, all the non-coterminal angles, (use arctan)
    x=0,180.
    Q.E.D.
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  5. #5
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    so more than one problem relating to the same topic counts as multiple posts?
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  6. #6
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    I saw that you made multiple posts on the topic of trigonometry. I do not think you want to "spam" the forum. I would allow it, but be careful and do not start asking the same question everywhere, because then we, the moderators, have to waste time deleting them. CaptainBlack already banned a person for 1 day for doing "spamming".
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  7. #7
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    Quote Originally Posted by ThePerfectHacker
    I saw that you made multiple posts on the topic of trigonometry. I do not think you want to "spam" the forum. I would allow it, but be careful and do not start asking the same question everywhere, because then we, the moderators, have to waste time deleting them. CaptainBlack already banned a person for 1 day for doing "spamming".
    I would not have banned them for posting the same question to multiple
    fora, at most I may have deleted all but one.

    The person in question posted exactly the same message 5 times (and may
    have been still posting copies when I banned them), and the message was
    not a question but publicity for their web site (admittedly mathematical).

    As it is I have left one copy of their message online.

    I must confess to being touchy about spam on message boards, and if I
    have the ability to stop it I will. I have seen enough good sites ruined by
    spam.

    RonL
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