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Math Help - Graphing the trig function from to given points?

  1. #16
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    Leave the answer in radical form unless told otherwise. It is easier to write and remember.
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  2. #17
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    \displaystyle -4 = \frac{a}{\sqrt{2}}.

    How do you undo dividing by \displaystyle \sqrt{2}?
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  3. #18
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    Quote Originally Posted by Prove It View Post
    \displaystyle -4 = \frac{a}{\sqrt{2}}.

    How do you undo dividing by \displaystyle \sqrt{2}?
    I guess I'm more of a visual learner, which is why I need to see the full problem worked out, study the process, understand the logic, and then apply what I learn.

    So (a = 4)

    I still would like to see the whole problem worked out for my notes. I still confused.
    Last edited by Smokinoakum; March 19th 2011 at 12:41 AM.
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  4. #19
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    note that a \ne 4


    -4 = \dfrac{a}{\sqrt{2}}

    to solve for a , multiply both sides by \sqrt{2} ...

    a = -4\sqrt{2}

    also, your instructor should have introduced you to the exact trig values of sine and cosine on the unit circle. (then you would have known the exact value of \sin\left(\frac{3\pi}{4}\right) w/o consulting your calculator)

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  5. #20
    Newbie Smokinoakum's Avatar
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    Quote Originally Posted by skeeter View Post
    note that a \ne 4


    -4 = \dfrac{a}{\sqrt{2}}

    to solve for a , multiply both sides by \sqrt{2} ...

    a = -4\sqrt{2}

    also, your instructor should have introduced you to the exact trig values of sine and cosine on the unit circle. (then you would have known the exact value of \sin\left(\frac{3\pi}{4}\right) w/o consulting your calculator)

    Very cool! That helps a lot.

    Well I entered in a = -4\sqrt{2} in my assignment and it said that it was wrong?

    The answer was (the function y = ( 4 ) sin x passes through (3pi/2 , -4)

    I think I've confused both myself and you generous people helping me out. Such is learning this stuff online and not in a class room.

    What have I missed here?
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  6. #21
    Newbie Smokinoakum's Avatar
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    Quote Originally Posted by Prove It View Post
    Like I said, substitute \displaystyle x = \frac{3\pi}{4} and \displaystyle y = -4 into the equation \displaystyle y = a\sin{x}.

    Surely you can go from there...
    This is where some of the confusion happened!

    He should have said "substitute \displaystyle x = \frac{3\pi}{2} and \displaystyle y = -4 into the equation"

    Not "substitute \displaystyle x = \frac{3\pi}{4} and \displaystyle y = -4 into the equation"

    So the equation should be \displaystyle -4 = a\ sin \frac{3\pi}{2} right?
    Last edited by Smokinoakum; March 19th 2011 at 11:24 AM.
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  7. #22
    Newbie Smokinoakum's Avatar
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    OK...going from what Prove It helped me out with, this is what I have figured out.

    Find the function of the form \displaystyle y =  a\ sin\ x that passes through \displaystyle \left(\frac{3\pi}{2}, -4\right)

    Substitute \displaystyle (x, y) = \left(\frac{3\pi}{2}, -4\right) into \displaystyle y=a\sin{x} and solve for \displaystyle a.

    \displaystyle -4 = a\ sin \frac{3\pi}{2}

    \displaystyle sin \frac{3\pi}{2}  =\ -1

    \displaystyle -4  =\frac{a}{-1}

    \displaystyle -4 (-1) =\ 4

    \displaystyle a =\ 4


    Does this follow the concept?
    Last edited by Smokinoakum; March 19th 2011 at 11:23 AM.
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  8. #23
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    Quote Originally Posted by Smokinoakum View Post
    OK...going from what Prove It helped me out with, this is what I have figured out.

    Find the function of the form \displaystyle y =  a\ sin\ x that passes through \displaystyle \left(\frac{3\pi}{2}, -4\right)

    Substitute \displaystyle (x, y) = \left(\frac{3\pi}{2}, -4\right) into \displaystyle y=a\sin{x} and solve for \displaystyle a.

    \displaystyle -4 = a\ sin \frac{3\pi}{2}

    \displaystyle sin \frac{3\pi}{2}  =\ -1

    \displaystyle -4  =\frac{a}{-1}

    \displaystyle -4 (-1) =\ 4

    \displaystyle a =\ 4


    Does this follow the concept?
    Sorry about the confusion before, thought it said \displaystyle x = \frac{3\pi}{4}.

    Yes, you have now correctly found \displaystyle a.

    So the equation of your function is \displaystyle y = 4\sin{x}. This is the same as the function \displaystyle \sin{x}, being stretched by a factor of \displaystyle 4 vertically.
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  9. #24
    Newbie Smokinoakum's Avatar
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    No worries about the confusion. It made me really try to fully grasp how these functions relate to one another. Thanks a lot for your help.

    It's great to have a place like this to come to when you take math courses online!
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