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March 26, 2017

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Find all values of theta in the interval 0 <= theta < 360 that satisfy the equation 3cos(2theta)=7cos(theta). Express answers to the nearest ten minutes.

  • Trig - ,

    Cos2T= sin^2T-Cos^2T=1-2cos^2T

    3-6cos^2T=7cosT

    let u=cosT

    6u^2+7u-3=0

    (3u-1)(2u+3)=0

    u= 1/3 u= -2/3
    so what angles are those?

  • Trig - ,

    3cos(2Ø)=7cos(Ø)
    3(2cos^2 Ø - 1) = 7cosØ
    6cos^ Ø - 7cosØ - 3 = 0
    (3cosØ+1)(2cosØ-3) = 0
    cosØ = -1/3 or cosØ = 3/2, the last is not possible

    cosØ = -1/3
    Ø must be in II or III
    Ø = 180 - 70.529 or Ø = 180 + 70.529
    = 109.471° or 250.053°

    I assume you know how to change those decimals to degrees and minutes.

  • Trig - ,

    I must respectfully disagree with bob

    cos 2T = cos^2 T - sin^2 T = 2cos^2 T - 1
    bob had it backwards, time for a strong coffee.

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