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Thread: Finding solutions

  1. #1
    Member
    Joined
    Nov 2008
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    103

    Finding solutions

    Find a solution to = -10/17 in the interval [, ] correct to two decimal places.

    How would you solve this? Cheers.
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  2. #2
    Member
    Joined
    Dec 2008
    Posts
    167
    $\displaystyle

    cos x = (-\frac{10}{17})
    $
    $\displaystyle
    x_{1} = 126.03^0 + k2\Pi
    $
    $\displaystyle
    x_{2} = 233.97^0 + k2\Pi
    $

    $\displaystyle
    19\Pi \leq x_{1,2} + k2\Pi \leq 20\Pi \Rightarrow 3420^0 \leq x_{1,2} + k \times 360^0 \leq 3600^0
    $

    from that you know that k is 9 because the solution needs to be in the $\displaystyle [19\Pi, 20\Pi]$ interval.

    if k = 9
    then

    $\displaystyle
    k2\Pi = 9 \times 2 \times 180^0 = 3240^0
    $

    $\displaystyle 3240^0 + x_{1} \leq 19\Pi$
    $\displaystyle 20\Pi \geq 3240^0 + x_{2} \geq 19\Pi$

    $\displaystyle x_{2} = 233,97^0$ is the solution.
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