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Math Help - 88sin(x) + 242cos(x) = 250

  1. #1
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    88sin(x) + 242cos(x) = 250

    solve this using algebra
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  2. #2
    Senior Member pacman's Avatar
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    88sin(x) + 242cos(x) = 250, solve for x

    __________________________________________________ _______

    use this identity: a sin x + b cos x = (a^2 + b^2)^1/2 sin (x + C),

    where C = arcsin (b/(a^2 + b^2)), for a is greater or less than 0, also

    = pi - arcsin (b/(a^2 + b^2)), for a less than 0.


    Then C1 = arcsin (b/(a^2 + b^2))

    = arcsin(242/(88^2 + 242^2)^1/2) = arcsin (11/sqrt 137)

    = 1.222 rad

    = 70.02 degrees

    C2 = pi - C1 = 180 - 72.02 degrees = 107.98 degrees

    Also, (a^2 + b^2)^1/2 sin (x + C) = (88^2 + 242^2)^1/2) sin (x + C)

    = 22 (sqrt 137) sin (x + C)

    = 257.5 sin (x + C)

    But, 257.5 sin (x + C) = 250, simplifying

    sin (x + C) = 250/257.5

    -------------------------------------------------------------------

    x1 + C1 = arcsin (250/257.5) = 76.14 degrees

    x1 = 76.14 - C1

    x1 = 76.14 - 70.02 = 6.12 degrees

    ------------------------------------------------------------------

    or equivalently,

    x2 = 76.14 - c2 = 76.14 - 107.98 = -31.84 degrees
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  3. #3
    Senior Member pacman's Avatar
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    88sin(x) + 242cos(x) = 250, solving this using algebra?

    what a tall order, a trigonometric function to BE solved by ALGEBRA.

    Any HINT?
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