Math - Trigonometry

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If sin theta +cos theta =1.2, then what is sin^3 theta + cos^3 theta?

Hmm...I don't understand how to proceed. I know I must apply a trig Identity, but which one?

Thanks in advance

  • Math - Trigonometry -

    sinØ + cosØ = 1.2
    square both sides
    sin^2 Ø + 2sinØcosØ + cos^2 Ø = 1.44
    but sin^2Ø + cos^2Ø = 1
    2sinØcosØ = 0.44
    sinØcosØ = .22

    now using the fact that

    (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
    we see that
    a^3 + b^3 = (a+b)^3 - 3a^2b - 3ab^2
    = (a+b)^3 - 3ab(a+b)

    so sin^3 Ø + cos^3 Ø
    = (sinØ + cosØ)^3 - 3sinØcosØ (sinØ + cosØ)
    = 1.2^3 - 3(.22)(1.2)
    = 0.936

    check:
    from 2sinØcosØ = .44
    sin 2Ø = .44
    2Ø = 26.103...
    Ø = 13.0519....
    then by calculator: sin^3 13.0519° + cos^3 13.0519°
    = .93599...
    not bad!

  • Math - Trigonometry -

    Thanks a lot :)

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