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Math Help - [SOLVED] Trig Functions

  1. #1
    Junior Member
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    Ornskoldsvik
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    Arrow [SOLVED] Trig Functions

    Hello mates, I would like some help with these problems,

    1. Solve tan(θ) + 1 = 0, 0 ≤ θ < 2pi

    2. Solve tan(θ) − 3cot(θ) = 0, 0 ≤ θ < 2pi

    3. Solve 2sin(θ) − √2tan(θ) = 0, 0 ≤ θ < 2pi

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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello OVechkin8
    Quote Originally Posted by OVechkin8 View Post
    Hello mates, I would like some help with these problems,

    1. Solve tan(θ) + 1 = 0, 0 ≤ θ < 2pi

    2. Solve tan(θ) − 3cot(θ) = 0, 0 ≤ θ < 2pi

    3. Solve 2sin(θ) − √2tan(θ) = 0, 0 ≤ θ < 2pi

    Have a great holiday break!
    What have you done to try to solve these?

    #1 is very simple: \tan \theta = -1. So ...?

    #2: \tan\theta -\frac{3}{\tan\theta}=0

    \Rightarrow \tan^2\theta - 3 = 0

    So ...?

    #3: 2\sin\theta -\frac{\sqrt2\sin\theta}{\cos\theta}=0

    \Rightarrow 2\sin\theta\cos\theta -\sqrt2\sin\theta=0

    \Rightarrow \sin\theta(2\cos\theta-\sqrt2)=0

    \Rightarrow \sin\theta = 0 or ...?

    Can you complete these now?

    Grandad
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  3. #3
    Senior Member nikhil's Avatar
    Joined
    Jun 2008
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    check this out

    1) tanx+1=0
    tanx=-1
    therfor
    x=3pi/4 or 7pi/4

    2)tanx-3cotx=0
    tanx-3/tanx =0
    (tanx)^2-3=0
    tanx=+-(3)^(1/2)
    therfor
    x= pi/3 or 4pi/3 or 2pi/3 or 5pi/3
    3) 2sinx-(sqrt2)tanx=0
    2sinx=(sqrt2)tanx
    2sinx=(sqrt2)sinx/cosx
    cosx = 1/(sqrt2)
    or sinx=0

    therfor
    either x=0 or
    x=pi/4 or 7pi/4
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  4. #4
    Junior Member
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    Ornskoldsvik
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    Thanks guys, for the last one it was, 0, pi, pi/4, and 7pi/4. SOLVED.
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