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Math Help - LAST one - Promise! Trigonometric Ecuations.

  1. #1
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    LAST one - Promise! Trigonometric Ecuations.

    I know that how to work with cos, sin and tan...

    taną2x + tanx = 0
    tanx(tanx + 1) = 0

    tanx = 0
    x = undefined

    tanx + 1 = 0
    tanx = -1
    x = -45


    But, how do I solve:

    (√3)csc(x) - 2 = 0


    Thank you!
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  2. #2
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    Hello, Polyxendi!

    \taną2\!x + \tan x \:=\: 0

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

    \tan x \:=\: 0 \quad\Rightarrow\quad x \:=\:\text{unde{f}ined} . . . . no . . {\color{red} x \:=\:\hdots\:\text{-}180^o,\:0^o,\:180^o,\:360^o,\:\hdots}

    \tan x + 1 \:=\: 0\quad\Rightarrow\quad \tan x \:=\: \text{-}1\quad\Rightarrow\quad{\color{blue} x \:=\:\hdots \text{-}225^o,\:\text{-}45^o,\:135^o,\:315^o,\:\hdots}


    But how do I solve: . \sqrt{3}\csc x - 2 \:=\: 0
    Same way . . .

    We have: . \sqrt{3}\csc x  \:=\:2 \quad\Rightarrow\quad \csc x \:=\:\frac{2}{\sqrt{3}}

    You're expected to recognize that as: x \,=\,60^o


    Therefore: . x \;=\;\hdots\:\text{-}240^o,\:60^o,\:120^o,\:420^o,\:\hdots

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  3. #3
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    Quote Originally Posted by Polyxendi View Post
    I know that how to work with cos, sin and tan...

    taną2x + tanx = 0
    tanx(tanx + 1) = 0

    were you given an interval to find solutions for x ?

    tanx = 0
    x = undefined no, that's not correct

    tanx + 1 = 0
    tanx = -1
    x = -45 that is one solution, x = what other values?


    But, how do I solve:

    (√3)csc(x) - 2 = 0

    \textcolor{red}{\csc{x} = \frac{2}{\sqrt{3}}}

    \textcolor{red}{\sin{x} = \frac{\sqrt{3}}{2}}

    solutions for the last equation are straight off the unit circle, which you have memorized, right ?

    .
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