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Thread: doing things in the right order

  1. #1
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    doing things in the right order

    Hi folks,

    I am trying to find the general solution to a trig equation:

    I get to $5 sin (\theta + 53.1\circ) = 1$

    so $(\theta + 53.1) = sin^{-1}(\frac{1}{5}) = 11.5\circ $

    so I think the general solution is $\theta + 53.1 = 180\circ n + (-1)^n 11.5\circ$

    i.e. $\theta = 180\circ n + (-1)^n -41.6\circ$

    the answer in my maths books is $360\circ n + 115.3\circ , 360\circ n - 41.6\circ$

    I can understand the second solution but not the first.

    I could have simplified the second equation to $\theta = -41.6$ with solutions at 41.6 and 221.6

    Or I could have $\theta + 53.1 = 11.54$ and $(180 - 11.5)$

    I am not sure which order to do things.
    Last edited by s_ingram; Aug 15th 2017 at 11:29 PM.
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  2. #2
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    Re: doing things in the right order

    $\sin(t+53.1)=\dfrac{1}{5} \implies (t+53.1)$ is an angle in quadrant I or II.

    for quadrant I ...

    $t+53.1 = \arcsin\left(\dfrac{1}{5}\right) + k \cdot 360$ where $k \in \mathbb{Z}$

    $t = -41.56 + k \cdot 360$


    for quadrant II ...

    $t+53.1 = 180 - \arcsin\left(\dfrac{1}{5}\right) + k \cdot 360$

    $t = 115.36 + k \cdot 360$
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  3. #3
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    Re: doing things in the right order

    Quote Originally Posted by s_ingram View Post
    Hi folks,

    I am trying to find the general solution to a trig equation:

    I get to $5 sin (\theta + 53.1\circ) = 1$

    so $(\theta + 53.1) = sin^{-1}(\frac{1}{5}) = 11.5\circ $

    so I think the general solution is $\theta + 53.1 = 180\circ n + (-1)^n 11.5\circ$
    Here is your error: (-1)^n(11.5)- 53.1 is not equal to (-1)^n(11..5- 53.1). The "(-1)^n" does not multiply -53.1.

    i.e. $\theta = 180\circ n + (-1)^n -41.6\circ$

    the answer in my maths books is $360\circ n + 115.3\circ , 360\circ n - 41.6\circ$

    I can understand the second solution but not the first.

    I could have simplified the second equation to $\theta = -41.6$ with solutions at 41.6 and 221.6

    Or I could have $\theta + 53.1 = 11.54$ and $(180 - 11.5)$

    I am not sure which order to do things.
    Thanks from s_ingram
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  4. #4
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    Re: doing things in the right order

    Only just noticed your post!
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