solve the equation for the exact solutions over the interval [0,2pi) 8 tan 3x= 8?

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  • Como
    Lv 7
    3 weeks ago

    -

    tan 3 x = 1

    3x = π/4 , 5π/4 , 9π/4 , 13π/4 , 17π/4 , 21π/4

    x = π/12 , 5π/12 , 3π/4 , 13π/12 , 17π/12 , 7π/4

  • 3 weeks ago

    tan3x = 1

    i.e. 3x = π/4 + nπ....for n = 0, 1, 2,...

    so, x = π/12 + nπ/3

    => x = π(1 + 4n)/12

    Then, with n = 0, 1, 2,...we have:

    x = π/12, 5π/12, 9π/12, 13π/12, 17π/12 and 21π/12...for [0, 2π)

    :)>

  • ted s
    Lv 7
    3 weeks ago

    hint : tan Θ = 1 ===> Θ = π / 4 + nπ

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