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Math Help - Trig Equations

  1. #1
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    Trig Equations

    solve each equation on the internal 0 is greater than equal to theta less than 2pie.

    10) (cot theta +1)(csc theta -1/2) = 0
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  2. #2
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    (\cot{\theta} + 1)(\csc{\theta} - \frac{1}{2}) = 0

    Solutions will be when \cot{\theta} = -1 and when \csc{\theta} = \frac{1}{2}.

    HOWEVER if \csc{\theta} = \frac{1}{2}, this implies \sin{\theta} = 2 which is invalid.

    So the only solutions are found by solving \tan{\theta} = -1 (because if \cot{\theta} = -1 then so does \tan{\theta})
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  3. #3
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    Quote Originally Posted by kukid123 View Post
    solve each equation on the internal 0 is greater than equal to theta less than 2pie.

    10) (cot theta +1)(csc theta -1/2) = 0
    Case 1: \cot \theta + 1 = 0 \Rightarrow \tan \theta = -1. Now solve this simple equation.

    Case 2: \csc \theta - \frac{1}{2} = 0 \Rightarrow \sin \theta = 2. Do you think there'll be real solutions here ....?
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  4. #4
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    Case 1: . Can you help on this one? I am not getting the message?

    Case 2: . OK so this one is obviously not Valid.
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  5. #5
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    Quote Originally Posted by kukid123 View Post
    Case 1: . Can you help on this one? I am not getting the message?

    [snip]
    Hint: \tan \frac{3 \pi}{4} = -1. Now use either the known period of \tan \theta or the symmetry of the unit circle to find the second value of \theta.

    You're expected to know these things. If you don't, then you should be reviewing earlier work on how to solve basic trig equations involving sin, cos and tan instead of attempting to solve the equations you've been posting.
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  6. #6
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    OK right so the answer would be (-sqrt2/2, sqrt2/2)?
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  7. #7
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    Right, you know that \cot{\theta} = -1, and you should know that \tan{\theta} = \frac{1}{\cot{\theta}}. So in this case \tan{\theta} = \frac{1}{-1} = -1

    You should know how to find the values for \theta in the interval 0 \leq \theta \leq 2\pi that satisfy this equation.

    You should have \theta = \left\{ \frac{3\pi}{4},~ \frac{7\pi}{4} \right\}
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