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Math Help - Rearranging

  1. #1
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    Rearranging

    Hi, have to rearrange this equation for t, but keep getting it wrong. Can anyone help? Thanks and my gratitude

    21=10 sin 10(t-9) + 11
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  2. #2
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    Quote Originally Posted by Alex1313 View Post
    Hi, have to rearrange this equation for t, but keep getting it wrong. Can anyone help? Thanks and my gratitude

    21=10 sin 10(t-9) + 11
    Hi and welcome!

    Which do you mean?

    21=10 \sin (10(t-9)) + 11

    or

    21=10 (\sin 10)(t-9) + 11

    ?
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  3. #3
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    first one. It should be 18. I just want to know how to solve for t with a trig function
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  4. #4
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    Quote Originally Posted by Alex1313 View Post
    first one. It should be 18. I just want to know how to solve for t with a trig function
    I don't know why it would be 18.

    21=10 \sin (10(t-9)) + 11

    10=10 \sin (10(t-9))

    1= \sin (10(t-9))

    10(t-9) = \frac{\pi}{2}+k\cdot2\pi, k\in\mathbb{Z}

    t=9+\frac{\pi}{20}+k\cdot\frac{\pi}{5}, k\in\mathbb{Z}
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    thanks anyways
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  6. #6
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    Quote Originally Posted by Alex1313 View Post
    thanks anyways
    Oh right, degrees.

    21=10 \sin (10(t-9)^\circ) + 11

    10=10 \sin (10(t-9)^\circ)

    1= \sin (10(t-9)^\circ)

    10(t-9)^\circ = 90^\circ+k\cdot360^\circ, k\in\mathbb{Z}

    t=18+k\cdot36, k\in\mathbb{Z}

    If you really wanted to you could write

    10(t-9)^\circ = 90^\circ+k\cdot360^\circ, k\in\mathbb{Z}

    as

    10(t-9)^\circ = \sin^{-1}(1)+k\cdot360^\circ, k\in\mathbb{Z}
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