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Math Help - Solving Trig equations

  1. #1
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    Solving Trig equations

    Solve for x: tan(3x)=-1 , 0≤x≤180

    I worked it out and I found x=7π/12. Because 7π/12 is out of the 0≤x≤180 interval, would that be my final answer?

    Thanks
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  2. #2
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    Re: Solving Trig equations

    Does the 3 call for me to increase my interval by 3 times making it 0≤x≤540 ?
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  3. #3
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    Re: Solving Trig equations

    tan ( 3x ) = -1 = tan ( pi - pi/4 ) = tan ( 3pi/4 ) that gives 3x = 3pi/4 and so x = pi/4
    also tan ( 3x ) = -1 = tan ( 2pi - pi/4 ) = tan ( 7pi/4 ) this implies 3x = 7pi/4 thus x = 7pi/12
    Now you can draw the correct conclusion
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  4. #4
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    Re: Solving Trig equations

    So the correct answer would be x=pi/4 because x=7pi/12 is not within the specified interval of 0≤x≤180?
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  5. #5
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    Re: Solving Trig equations

    Hi Curt26,

    Quote Originally Posted by curt26 View Post
    Does the 3 call for me to increase my interval by 3 times making it 0≤x≤540 ?
    No.

    question specifically mentions your domain of x.

    its not possible to change the domain.

    the only difference that 3x does is to make you include some more values of x

    Quote Originally Posted by curt26 View Post
    So the correct answer would be x=pi/4 because x=7pi/12 is not within the specified interval of 0≤x≤180?
    pi= 180 degrees

    what's the value of 7pi/12

    --------------------------

    dont be afraid to have multiple answers.

    x can have multiple values.

    Cheers
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  6. #6
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    Re: Solving Trig equations

    Hello, curt26!

    \text{Solve: }\:\tan(3x)\,=\,\text{-}1\qquad 0 \le x\le \pi

    \text{Does the "3" call for me to increase my interval making it }0 \le {\color{red}3}x \le 3\pi\,? \;\;\;\color{blue}{\text{Yes!}}

    We have: . \tan(3x) \:=\:\text{-}1

    Then: . 3x \:=\:\frac{3\pi}{4},\;\frac{7\pi}{4},\;\frac{11\pi  }{4}

    Therefore: . x \;=\;\frac{\pi}{4},\;\frac{7\pi}{12},\;\frac{11\pi  }{12}
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