Trigonometry

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4+29sin=12cos^2

How do you determine this

  • Trigonometry -

    If your expression mean:

    4+29sin(x)=12cos^2(x)

    then go on:

    wolframalpha dot com

    When page be open in rectangle type:

    solve 4+29sin(x)=12cos^2(x)

    and click option =

    After few seconds when you see result click option: Show steps

  • Trigonometry -

    Remark:

    cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )


    12 cos ^ 2 ( x )= 12 [ 1 - sin ^ 2 ( x ) ] =

    12 - 12 sin ^ 2 ( x )


    29 sin ( x ) - 12 cos ^ 2 ( x ) + 4 =

    29 sin ( x ) - [ 12 - 12 sin ^ 2 ( x ) ] + 4 =

    29 sin ( x ) - 12 + 12 sin ^ 2 ( x ) + 4

    = 29 sin ( x ) - 8 + 12 sin ^ 2 ( x ) =

    12 sin ^ 2 ( x ) + 29 sin ( x ) - 8

  • Trigonometry -

    When I solved this out I got x=-32/12 and x=1/4. Is this right?

  • Trigonometry -

    Not x = .... but rather sinx = -32/12 or sinx = 1/4

    Picking up from where Bosnian left off
    12sin^2 x+ 29sinx - 8 = 0
    (4sinx - 1)(3sinx + 8) = 0

    sinx = 1/4 or sinx = -8/3, but sinx has to be between -1 and 1, so the last part is undefined

    sinx = 1/4, so
    x = 14.48° or 165.52°

    if you want radians, set your calculator to RAD
    and find arcsin (.25)

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