trigonometry

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Solve the equation 6 cos x^2+sin x=4 if 0 is less than or equal to x is less than or equal to pi

  • trigonometry -

    6 cos ^ 2 ( x ) + sin ( x ) = 4

    Then :

    6 * [ 1 - sin ^ 2 ( x ) ] + sin ( x )= 4

    6 - 6 sin ^ 2 ( x ) + sin ( x ) = 4

    - 6 sin ^ 2 ( x ) + sin ( x ) + 6 - 4 = 0

    - 6 sin ^ 2 ( x ) + sin ( x ) + 2 = 0

    Substitution :

    sin ( x ) = u

    - 6 u ^ 2 + u + 2 = 0

    The exact solutions are :

    u = 2 / 3

    and

    u = - 1 / 2


    OR

    sin ( x ) = 2 / 3

    and

    sin ( x ) = - 1 / 2


    sin ^ - 1 ( 2 / 3 ) = 0.729728 radians


    sin ^ - 1 ( - 1 / 2 ) = - pi / 6 radians


    The period of sine function is 2 pi.


    If :

    0 ¡Ü x

    Solution are :

    x = 2 n pi + ( - pi / 6 ) =

    2 n pi - pi / 6

    where n is an integer


    P.S.

    If you don't know how to solve equation :

    - 6 u ^ 2 + u + 2 = 0

    Then in google type:

    quadratic equation online

    When you see list of results click on:
    Free Online Quadratic Equation Solver:Solve by Quadratic Formula

    When page be open in rectangle type:

    - 6 u ^ 2 + u + 2 = 0

    and click option: solve it

    You will see solution step-by step

  • trigonometry -

    ¡Ü

    mean less than or equal to

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