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Math Help - Linear Trig Equation help plz!

  1. #1
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    Linear Trig Equation help plz!

    2. Find all solutions of each equation.
    a) cot x = 2.3 (I can find it with special angles, but not this)
    b) 5 cos 3x = -3

    3. c) 2sinx - 1 = -2

    You people here are very kind! Thanks!
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  2. #2
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    a)
    \cot\alpha=\tan\left(90^\circ-\alpha\right)
    90^\circ-x=\arctan 2.3 \approx 66.5^\circ + k\cdot 180^\circ \rightarrow x\approx 23.5^\circ + k\cdot 180^\circ ( \forall k \in \mathbb{Z})

    b)
     x=\frac{\arccos\frac{-3}{5}}{3}\approx \frac{\pm 126.87+k\cdot 360^\circ}{3}\approx \pm 42.29 + k\cdot 120^\circ ( \forall k \in \mathbb{Z})

    c) 2\sin x=-1
    x=\arcsin\frac{-1}{2}=-30^\circ + k\cdot 360^\circ or 180^\circ -(-30^\circ) + k\cdot 360^\circ = 210^\circ + k\cdot 360^\circ ( \forall k \in \mathbb{Z})
    Or if it should be 2\sin (x-1)=-2 then x-1=\arcsin-1=-90^\circ + k\cdot 360^\circ or  270^\circ + k\cdot 360^\circ \rightarrow x=-89^\circ + k\cdot 360^\circ or 269^\circ + k\cdot 360^\circ ( \forall k \in \mathbb{Z})


    Please correct me if I'm wrong!
    Last edited by james_bond; November 15th 2007 at 09:16 AM.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by finalfantasy View Post
    a) cot x = 2.3
    Quote Originally Posted by james_bond View Post
    a)
    \cot\alpha=\tan\left(90^\circ-\alpha\right)
    90^\circ-x=\arctan 2.3 \approx 66.5^\circ + k\cdot 180^\circ \rightarrow x\approx 23.5^\circ + k\cdot 180^\circ ( \forall k \in \mathbb{Z})
    It is simpler to note that
    cot(x) = \frac{1}{tan(x)} = 2.3

    So
    x = tan^{-1} \left ( \frac{1}{2.3} \right )

    -Dan
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