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Math Help - trigonometry question

  1. #1
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    trigonometry question

    find all solutions of the equation in the interval [0, 2pi)

    tan^2 x + tan x = 0

    I am not quite sure how to find the solutions for the tan. I think I am supposed to use the sum and difference formula to solve the problem.

    tan(u + v) = (tan u + tan v) / (1 - tan u tan v)

    is this correct?
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  2. #2
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    Hello, robasc!

    Find all solutions in the interval [0,\:2\pi)\!:\;\;\tan^2\!x + \tan x \:= \:0
    You forgot the most basic method for solving equations:
    . . Factor, set each factor equal to zero, and solve.


    Factor: . \tan x(\tan x + 1) \:=\:0


    Then: . \tan x \:=\:0 \quad\Rightarrow\quad x \:=\:0,\:\pi

    And: . \tan x + 1 \:=\:0 \quad\Rightarrow\quad \tan x \:=\:-1 \quad\Rightarrow\quad x \:=\;\frac{3\pi}{4},\:\frac{7\pi}{4}

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