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Math Help - Find the angles

  1. #1
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    Find the angles

    Find the angle Θ, 0 Θ ≤ 2 pi

    Cos Θ = 0.2157 Tan Θ =-0.7147

    The answers I were given show 2 answers can be found. Can someone tell me the answers for both questions and explain how it can be found.

    THANK YOU.
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  2. #2
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    Hello, finalfantasy!

    Find the angle \theta,\;\;0 \leq \theta \leq 2\pi

    . . \cos\theta = 0.2157,\;\;\tan\theta = -0.7147

    The answers show two answers can be found. . ??

    Only one angle is possible.

    Cosine is positive in Quadrants 1 and 4.
    Tangent is negative in Quadrants 2 and 4.
    . . Hence, \theta is in Quadrant 4 . . . so where's the other angle?

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  3. #3
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    Those are 2 separate questions ^^;

    Sorry about that.

    1. Cos Θ = 0.2157

    2. Tan Θ =-0.7147
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  4. #4
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    Hello, finalfantasy!

    Don't you have inverse trig functions on your calculator?


    1.\;\;\cos\theta \:=\:0.2157

    \theta \:=\:\cos^{-1}(0.2157) \;\approx\;1.35,\;4.93 radians



    2.\;\;\tan\theta \:=\:0.7147

    \theta \:=\:\tan^{-1}(0.7147) \:\approx\:0.62,\;3.76 radians

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  5. #5
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    Hmm ... those were the answers on my sheet, I got the first answer for each of those questions, but how do you get the second? o-o;
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  6. #6
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    Quote Originally Posted by finalfantasy View Post
    Find the angle Θ, 0 Θ ≤ 2 pi

    Cos Θ = 0.2157 Tan Θ =-0.7147

    The answers I were given show 2 answers can be found. Can someone tell me the answers for both questions and explain how it can be found.

    THANK YOU.
    Use the inverse function in your calculator,

    1. Cos^{-1}(0.2157) = 78
    2. Tan^{-1}(-0.7147) = -36

    I think you want the answer in both approximate and exact form, right? Or, find the two angles?

    To find the radians, you must convert degrees to radians, to do so:
    (degree) x (pi / degree)
    If you want to find the degrees from radians:
    (radian) x (degree / pi)

    1. Cos^{-1}(0.2157) = 78

    78 x pi/180
    = 78pi/180
    =13pi/30 or 1.36 rad

    To find the other angle in quadrant 4, you do your principle angle:
    360 -
    Θ
    = 360 - 78
    = 282

    282 x pi/180
    = 282pi/180
    = 14pi/9 or 4.89 rad



    2. Tan^{-1}(-0.7147) = -36

    Since the degree is a negative, the angle will be in the second and fourth quadrant because in the first and third quadrant, the angle would be in positive, hence, CAST rule

    First, you must find your related angle, which is 36 in this case

    36 x pi/180
    = 36pi/180
    = pi/5 or 0.63 rad

    To find the other radian, again, you must do your principle angle
    360 -
    Θ
    = 360 - 36
    = 324

    324 x pi/180
    = 9pi/5 or 5.65 rad
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