math

sinA=.....+cosA

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  1. I did this yesterday

    http://www.jiskha.com/display.cgi?id=1459511832

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    posted by Reiny
  2. Ok, how about this approach

    sinA = x + cosA
    x = sinA - cosA

    let's change sinA - cosA into a single sinusoidal expression:

    Let sinA - cosA = a sin(A + k)

    a sin(A+k)
    = a(sinAcosk + cosAsink_
    = asinAcosk + acosAsink

    then asinAcosk = sinA
    acosk = 1
    cosk = 1/a

    acosAsink = -cosA
    asink = -1
    sink = -1/a

    but we know sin^2 k + cos^2 k = 1
    (-1/a)^2 + (1/a)^2 = 1
    2/a^2 = 1
    a^2 = 2
    a = sqrt(2)

    also tank = sink/cosk = (-1/a) / (1/a) = -1
    k = -Pi/4

    so sinA - cosA = sqrt(2) sin(A - Pi/4)

    x = sqrt(2) sin(A - Pi/4)

    so I plotted on Wolfram:
    y = sinx - cosx and y = sqrt(2) sin(x - Pi/4)
    and the two curves coincides

    https://www.wolframalpha.com/input/?i=plot+y+%3D+sinx+-+cosx,+y+%3D+sqrt(2)+sin(x+-+Pi%2F4)

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    posted by Reiny

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