math

posted by Anonymous

Use the appropriate sum/difference formula to find the exact value of cos(105°).

do we choose one, then make 1 side equal cos of 105°? I don't understand the question.

  1. Bosnian

    105 ° = 210 ° / 2

    210 ° = 180 ° + 30 °


    cos ( A + B ) = cos ( A ) * cos ( B ) - sin ( A ) * sin ( B )


    sin 30 ° = 1 / 2

    sin 180 ° = 0

    cos 30 ° = sqrt ( 3 ) / 2

    cos 180 ° = - 1


    cos 210 ° = cos ( 180 ° + 30 ° ) = cos 180 ° * cos 30 ° - sin 180 ° * sin 30 ° =

    ( - 1 ) * sqrt ( 3 ) / 2 - 0 * 1 / 2 =

    - sqrt ( 3 ) / 2 - 0


    cos 210 ° = - sqrt ( 3 ) / 2


    cos ( theta / 2 ) = ± sqrt [ ( 1 / 2 ) * ( 1 + cos ( theta )) ]

    cos 105 ° = cos ( 210 ° / 2 ) =

    ± sqrt [ ( 1 / 2 ) * ( 1 + ( - sqrt ( 3 ) / 2 ) ] =

    ± sqrt [ ( 1 / 2 ) * ( 2 / 2 + ( - sqrt ( 3 ) / 2 ) ] =

    ± sqrt [ ( 1 / 2 ) * ( ( 2 - sqrt ( 3 ) / 2 ) ) ] =

    ± sqrt [ ( ( 2 - sqrt ( 3 ) ) / 4 ] =

    ± ( 1 / 2 ) sqrt [ 2 - sqrt ( 3 ) ] =

    ± sqrt [ 2 - sqrt ( 3 ) ] / 2



    The angle 105 ° is in the II quadrant

    In quadrant II cosine is negative.

    So

    cos ( 105 ° ) = - sqrt [ 2 - sqrt ( 3 ) ] / 2

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