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Math Help - What does tan θ<0 mean?

  1. #1
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    What does tan θ<0 mean?

    cosec θ= 1.115. Find sec θ while tan θ<0

    sin θ=0.89686
    θ =63.7484, 116.2515

    sec θ= 2.261,-2.261
    tan θ= 2.027, -2.027

    So is the answer -2.261? What does the tan θ<0 mean?
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  2. #2
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    Re: What does tan θ<0 mean?

    Quote Originally Posted by fuzzy View Post
    cosec θ= 1.115. Find sec θ while tan θ<0

    sin θ=0.89686
    θ =63.7484, 116.2515

    sec θ= 2.261,-2.261
    tan θ= 2.027, -2.027

    So is the answer -2.261? What does the tan θ<0 mean?
    Where is \displaystyle \tan{\theta} < 0?
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  3. #3
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    Re: What does tan θ<0 mean?

    It isn't stated
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  4. #4
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    Re: What does tan θ<0 mean?

    Quote Originally Posted by fuzzy View Post
    It isn't stated
    Think of the unit circle, for what values of \displaystyle \theta is \displaystyle \tan{\theta} negative?
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  5. #5
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    Re: What does tan θ<0 mean?

    Okay, so the θ will be in Q2 and Q4? So the θ I will be using is 116.2515 and 296.216?
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  6. #6
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    Re: What does tan θ<0 mean?

    Quote Originally Posted by fuzzy View Post
    Okay, so the θ will be in Q2 and Q4? So the θ I will be using is 116.2515 and 296.216?
    Almost, you also know that \displaystyle \sin{\theta} > 0. So where is \displaystyle \sin{\theta} > 0 AND \displaystyle \tan{\theta} < 0?
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