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Math Help - Need help on solving Trig equations

  1. #1
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    Question Need help on solving Trig equations

    Hello,
    I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:
    find all solutions ofin the interval [0,2pie) x representing theta.
    sin(x)cos(3x)+cos(x)sin(3x)=0

    cos(x)+sin(x)=0

    cos(x/2)-1=2

    2sin^2(x)=sin(x)

    cos(2x)=sin(x)

    cos(2x)=squareerootof 2 -cos(2x)

    If anyone could explain the steps and how to solve these it would be greatly appreciated.

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  2. #2
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    Quote Originally Posted by ConfusedMath View Post
    Hello,
    I am taking a precalc class and am having trouble when it comes to solving trig equations. Our book does not do a very good job on explaining and I have been unable to find any examples or similar problems to the following:
    find all solutions ofin the interval [0,2pie) x representing theta.
    sin(x)cos(3x)+cos(x)sin(3x)=0

    note the pattern ... sin(a)cos(b)+cos(a)sin(b) = sin(a+b)

    cos(x)+sin(x)=0

    this is just general knowledge of the unit circle ... at what angles does cos(x) = -sin(x) ??

    cos(x/2)-1=2

    cos(x/2) = 3

    what is the range of cos(anything) ?


    2sin^2(x)=sin(x)

    2sin^2(x) - sin(x) = 0

    factor and solve

    cos(2x)=sin(x)

    1 - 2sin^2(x) = sin(x)

    0 = 2sin^2(x) + sin(x) - 1

    factor and solve


    cos(2x)=squareerootof 2 -cos(2x)

    2cos(2x) = sqrt(2)

    cos(2x) = sqrt(2)/2

    look at your unit circle

    ...
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  3. #3
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    Thank you so much!!
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