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Math Help - find an angle from cosec and tan

  1. #1
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    Exclamation find an angle from cosec and tan

    Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
    value of the angle θ in radians. Justify your answer.

    so far i know that
    sin θ = -1/2 θ = -π/6
    tan θ = 1/√3 θ = π/6

    from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?

    any help would be great, thanks!
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  2. #2
    Member sbhatnagar's Avatar
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    Re: find an angle from cosec and tan

    Quote Originally Posted by gurnster76 View Post
    Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
    value of the angle θ in radians. Justify your answer.

    so far i know that
    sin θ = -1/2 θ = -π/6
    tan θ = 1/√3 θ = π/6

    from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?

    any help would be great, thanks!
    Yes. Solution of first eq. is -\frac{\pi}{6} and solution of second eq. is \frac{\pi}{6}.
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  3. #3
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    Re: find an angle from cosec and tan

    im asked to find the exact value, my question is; as its in the third quadrant is the answer π/6 not -π/6?
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  4. #4
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    Re: find an angle from cosec and tan

    Quote Originally Posted by gurnster76 View Post
    Given that cosec θ = −2, tan θ = 1/3√3 and −π < θ < π, find the exact
    value of the angle θ in radians. Justify your answer.

    so far i know that
    sin θ = -1/2 θ = -π/6
    tan θ = 1/√3 θ = π/6

    from this i know that its in the third quadrant, does this mean the angle in radians im looking for is π/6?
    to satisfy both of the given ratios in the given interval ...

    \theta = -\frac{5\pi}{6}
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