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Thread: Solving trig functions...

  1. #1
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    Question Solving trig functions...

    I am having trouble with this problem...It goes as follows:

    Find the exact value of:
    sin(2x), cos(2x), and tan(2x) if cos(x) = -4/5, [pi]/2 <x<[pi].

    It gives me a hint saying( sin2x=2sinxcosx and cos(2x)=2cos^2 (X-1)

    I have no idea how to do this Anyone care to help?
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  2. #2
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    Hello KAY03
    Quote Originally Posted by KAY03 View Post
    I am having trouble with this problem...It goes as follows:

    Find the exact value of:
    sin(2x), cos(2x), and tan(2x) if cos(x) = -4/5, [pi]/2 <x<[pi].

    It gives me a hint saying( sin2x=2sinxcosx and cos(2x)=2cos^2 (X-1)

    I have no idea how to do this Anyone care to help?
    First, note that, if $\displaystyle \pi/2 <x<\pi/2$, then $\displaystyle \sin x$ is positive.

    Then, using $\displaystyle \sin^2x =1-\cos^2x$, plug in the value $\displaystyle \cos x = -\tfrac45$:
    $\displaystyle \sin^2x=1 - \tfrac{16}{25} $
    $\displaystyle =\tfrac{9}{25}$
    $\displaystyle \Rightarrow\sin x = \tfrac35$ (taking the positive square root, since, as we said, $\displaystyle \sin x > 0$)
    Now you can simply plug in the values $\displaystyle \sin x = \tfrac35$ and $\displaystyle \cos x = -\tfrac45$ into the formulae that you've been given. The first one is:
    $\displaystyle \sin 2x =2\sin x \cos x$
    $\displaystyle =2\cdot\tfrac35\cdot(-\tfrac45)$

    $\displaystyle = ...$ ?
    Do $\displaystyle \cos 2x$ in the same way, using the formula:
    $\displaystyle \cos2x=2\cos^2x -1$
    Finally, use $\displaystyle \tan2x = \frac{\sin2x}{\cos2x}$ to find $\displaystyle \tan2x$.

    Can you complete them now?

    Grandad
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  3. #3
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    reply

    Just to make sure I did it right..my final answers are

    sin2x= -24/25
    cos2x=7/25
    tan2x=-24/7

    Am I correct?
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  4. #4
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    Hello KAY03
    Quote Originally Posted by KAY03 View Post
    Just to make sure I did it right..my final answers are

    sin2x= -24/25
    cos2x=7/25
    tan2x=-24/7

    Am I correct?
    Correct! Good work.

    Grandad
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