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Math Help - Finding sin and tan from secant?

  1. #1
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    Question Finding sin and tan from secant?

    If secθ = 17, what is sinθ? tanθ?

    In order to do this would we have to draw a triangle? Secant is hyp/opp. Thus should the hyp be 17 and the opp be 1?

    If that is the case will the answer be sinθ = 16.97/17 and tanθ = 16.97/1 = 16.97?

    PS: I got the 16.97 from using the a^2 + b^2 = c^2 formula. Please tell me if this is correct or is there something else to it. Thank you so much.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by nox16 View Post
    If secθ = 17, what is sinθ? tanθ?

    In order to do this would we have to draw a triangle? Secant is hyp/opp. Thus should the hyp be 17 and the opp be 1?

    If that is the case will the answer be sinθ = 16.97/17 and tanθ = 16.97/1 = 16.97?

    PS: I got the 16.97 from using the a^2 + b^2 = c^2 formula. Please tell me if this is correct or is there something else to it. Thank you so much.
    sec\theta = \frac{\text{hypotenuse(h)}}{\text{base(b)}} = \frac{17}{1}

    \therefore by Pythagorean theorem:

     h^2= p^2+ b^2

    find out what the perpendicular would be!

    then, use:

    sin\theta = \frac{\text{perpendicular(p)}}{\text{hypotenuse(h)  }}

    and

    tan\theta =\frac{\text{perpendicular(p)}}{\text{base(b)}}
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  3. #3
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    I think that what I am doing. I realized I made a mistake typing out the secantθ formula. It is actually adjacent/hyp.
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by nox16 View Post
    I think that what I am doing. I realized I made a mistake typing out the secantθ formula. It is actually adjacent/hyp.
    wait..

    adjacent/hyp = cosine(theta). secant is its reciprocal.

     sec\theta = \frac{\text{hypotenuse(h)}}{\text{adjacent(b)}}

    See this if you are not clear yet:

    Trigonometric functions - Wikipedia, the free encyclopedia
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  5. #5
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    Thanks for your help nonetheless.

    *Dang keep on messing up on these trig functions. I got it correctly on paper though.
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