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Math Help - Trigonometry (Pre-Cal)

  1. #1
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    Trigonometry (Pre-Cal)

    Hello helpers!

    I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

    It reads-

    Factor and simplify the following:

    tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

    then

    Find ALL solutions. No restrictions.

    2sin[^2]2x=1




    Thank you for those of you who try to help me out! You are greatly appreciated!

    -Margo
    Last edited by margo98; February 19th 2009 at 04:50 PM. Reason: figured out one of the problems
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by margo98 View Post
    Hello helpers!

    I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

    It reads-

    Factor and simplify the following:

    tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

    then

    Find ALL solutions. No restrictions.

    2sin[^2]2x=1




    Thank you for those of you who try to help me out! You are greatly appreciated!

    -Margo

    For the first one:
    first factor out the tan\theta

    So,

    tan\theta(sin^2 \theta + cos^2 \theta)

    Remember that sin^2\theta + cos^2 \theta = 1
    Can you finish this one?
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  3. #3
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    Here's the 2nd part:

    2\sin^2{2x}=1
    \sin{2x}=\pm\frac{1}{\sqrt{2}}
    since \sin{\frac{(2n+1)\pi}{4}}=\pm\frac{1}{\sqrt{2}};n=  0,1,2,3,...
    2x=\frac{(2n+1)\pi}{4}
    x=\frac{(2n+1)\pi}{8}
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  4. #4
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    Quote Originally Posted by margo98 View Post
    Hello helpers!

    I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

    It reads-

    Factor and simplify the following:

    tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

    \tan{t}(\sin^2{t} + \cos^2{t})

    you should know what \sin^2{t} + \cos^2{t} equals.


    then

    Find ALL solutions. No restrictions.

    2sin[^2]2x=1

    \sin^2(2x) = \frac{1}{2}

    \sin(2x) = \pm \frac{1}{\sqrt{2}}

    2x = odd multiples of \frac{\pi}{4}

    x = odd multiples of \frac{\pi}{8}
    hope it helps
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