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Math Help - Solving Trigonometric Equations

  1. #1
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    Solving Trigonometric Equations

    Solve this trigonometric equation 0^o {\leq} x {\leq} 360^o

    cos^2x+7sinxcosx=3

    Find the value of x (in degrees).
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  2. #2
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    Quote Originally Posted by acevipa View Post
    Solve this trigonometric equation 0^o {\leq} x {\leq} 360^o

    cos^2x+7sinxcosx=3

    Find the value of x (in degrees).
    \Rightarrow 2 \cos^2 x + 14 \sin x \cos x = 6

    \Rightarrow (\cos (2x) + 1) + 7 \sin (2x) = 6

    \Rightarrow \cos (2x) + 7 \sin (2x) = 5.

    There is a standard technique for converting the left hand side into the form A \sin (2x + \phi). Can you do that (read http://www.mathcentre.ac.uk/resource...a-alphaetc.pdf ). Then the equation becomes

    \sin (2x + \phi) = \frac{5}{A}

    which is easy.
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