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sin(x)+cos(x)=2/3

find the value of

sin(x)

  • Maths -

    square both sides
    sin^2 x + 2sinxcosx + cos^2 x = 4/9
    1 + sin 2x = 4/9
    sin 2x = -5/9

    2x = 213.75 or 2x = 326.25
    x = 106.87º or x = 163.126º

    but since we performed a "squaring" operation we have to verify each answer.

    when x = 106.87 , sin106.87 + cos106.87 = .66676.., so that works

    but for x= 163.126, the result was -.66676 which is NOT the right side

    so sinx = sin106.87 = .9569

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