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trig

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Find the exact value of the trigonometric function. -cot(pi/4 + 16pi)

  • trig -

    16π is the same as exactly 8 rotations, so
    -cot(π/4 + 16π) = -cot(π/4)
    = -1/tan(π/4) = -1/1 = -1

  • trig -

    cot ( A + B ) = 1 / tan ( A + B )

    tan ( A + B )= ( tanA + tanB )/( 1 - tanA * tanB )


    In this case:

    A = pi / 4

    B = 16 pi


    tan ( pi / 4 ) = tan 45° = 1

    tan ( 16 pi )= cot ( 8 * 2 pi ) = tan ( 8 * 360° ) = 0


    tan ( pi / 4 + 16 pi ) =

    [ ( tan ( pi / 4 ) + tan ( 16 pi ) ]/[ 1 - tan( pi / 4 ) * tan ( 16 pi ) ] =

    ( 1 + 0 ) / ( 1 - 1 * 0 ) =

    1 / ( 1 - 0 ) =

    1 / 1 = 1


    tan ( pi / 4 + 16 pi ) = 1


    cot ( pi / 4 + 16 pi ) =

    1 / tan ( pi / 4 + 16 pi ) =

    1 / 1 = 1


    - cot ( pi / 4 + 16 pi ) = - 1

  • trig -

    tan ( 16 pi )= tan ( 8 * 2 pi ) = tan ( 8 * 360° ) = 0

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