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Math Help - find a and b

  1. #1
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    find a and b

    Let f(x) = A sin ((2pi/B)*X)
    .The graph of this function has a tangent line with a slope of 4
    at the point (B/8 , 1)
    find the exact values of a and b

    so for a i put in B/8 for x and 1 for y and cancled out the b's and got
    a= 1/sin(pi/4)

    then for b do i find the derivative and make that = 4?
    or is b infinate?
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by valvan View Post
    Let f(x) = A sin ((2pi/B)*X)
    .The graph of this function has a tangent line with a slope of 4
    at the point (B/8 , 1)
    find the exact values of a and b

    so for a i put in B/8 for x and 1 for y and cancled out the b's and got
    a= 1/sin(pi/4)

    then for b do i find the derivative and make that = 4?
    or is b infinate?
    That's a good start and looks ok. Remember that \sin \left(\frac{\pi}{4}\right) = \frac{1}{\sqrt2} and hence \csc  \left(\frac{\pi}{4}\right) = \sqrt{2}<br />

    f'(x) = 4

    \frac{d}{dx} \left[ \sqrt2 \sin \left(\frac{2\pi x}{B}\right) \right]

    = \frac{2 \pi \sqrt{2} }{B} \cos \left(\frac{2\pi x}{B}\right) = 4

    It appears you'll need to use an iterative method
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