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Thread: Linear Trig Functions help please!

  1. #1
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    Linear Trig Functions help please!

    hey! can anybody please help me solve this question please!
    2Cos(x/2)=square root two
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  2. #2
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    or this question:
    5cos3x=-3
    thank-you!please reply!
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  3. #3
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    Hello, Jane!

    $\displaystyle 2\cos\left(\frac{x}{2}\right)\;=\;\sqrt{2}$

    Divide by 2: .$\displaystyle \cos\left(\frac{x}{2}\right) \:=\:\frac{\sqrt{2}}{2}$

    Now what angle has a cosine of $\displaystyle \frac{\sqrt{2}}{2}$ ?
    . . That's right . . . $\displaystyle \pm\frac{\pi}{4} + 2\pi n$

    So we have: .$\displaystyle \frac{x}{2} \:=\:\frac{\pi}{4} + 2\pi n$

    Therefore: .$\displaystyle \boxed{x \:=\:\frac{\pi}{2} + 4\pi n}$



    $\displaystyle 5\cos(3x)\:=\:-3$
    We have: .$\displaystyle \cos(3x) \:=\:\text{-}\frac{3}{5}$

    Then: .$\displaystyle 3x \:=\:\cos^{\text{-}1}\left(\text{-}\frac{3}{5}\right)$

    Therefore: .$\displaystyle \boxed{x \;=\;\frac{1}{3}\cos^{\text{-}1}\left(\text{-}\frac{3}{5}\right)}$

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  4. #4
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    thanks a lot!
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