trig

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if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta

  • trig -

    0.6 cosè + 0.8 sinè = 0.9
    Let sinx = 0.6; then
    cosx = 0.8 and x = 36.87 degrees
    sinx cosè + cosx sinè = 0.9
    sin (x + è) = 0.9
    x + è = 64.16 degrees or 115.84 degrees
    alpha = è1 = 27.29 degrees
    beta = è2 = 78.97

    alpha + beta = 106.26 degrees

    sin (alpha + beta) = 0.9600

  • trig -

    drwls,
    that is amazingly clever.

  • trig -

    thank you very much. can u solve the same by quadratic equation method

  • trig -

    yes, it can be done that way, but I'd rather leave that to you.

    Write it as

    6cosθ= 9 - 8 sinθ

    Square both sides and the left side can be written 36(1 - sin^2 θ)

    Then you have a quadratic in sin theta to solve. Have fun.

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