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Thread: Trigonometry involving Theta

  1. #1
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    Trigonometry involving Theta #2

    So my teacher is bad at explaining so I need your help.

    1. If cosθ = $\displaystyle \dfrac{1}{3}$ and 0 ≤ 2θ ≤ , find sin θ.

    2. Find all θ in the interval [0,2) that satisfy the equation: sinθ = $\displaystyle \dfrac{1}{2}$.
    Number 2 is suppose to be:
    Find all θ in the interval [0,2) that satisfy the equation: $\displaystyle \sin {\theta} - \sin {\theta} \cot {\theta} = 0$



    Tips are kind of helpful, but step-by-step views will surely help in understanding it thoroughly...
    Thank You!
    Last edited by meiyukichan; Nov 30th 2008 at 08:39 PM.
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  2. #2
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    Quote Originally Posted by meiyukichan View Post
    So my teacher is bad at explaining so I need your help.

    1. If cosθ = $\displaystyle \dfrac{1}{3}$ and 0 ≤ 2θ ≤ , find sin θ.

    2. Find all θ in the interval [0,2) that satisfy the equation: sinθ = $\displaystyle \dfrac{1}{2}$.


    Tips are kind of helpful, but step-by-step views will surely help in understanding it thoroughly... if that makes sense.
    Thank You!
    2.

    Keep in mind that saying $\displaystyle \sin{\theta}=\frac{1}{2}$ is the exact same as $\displaystyle \sin^{-1}(\frac{1}{2})=\theta$ which literally says "find the angle $\displaystyle \theta$ whose sine equals $\displaystyle \frac{1}{2}$.

    Also, think about the unit circle...where is the sine function positive? You are only going to have two answers on the interval $\displaystyle [0,2\pi)$
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  3. #3
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    Quote Originally Posted by elizsimca View Post
    2.

    Keep in mind that saying $\displaystyle \sin{\theta}=\frac{1}{2}$ is the exact same as $\displaystyle \sin^{-1}(\frac{1}{2})=\theta$ which literally says "find the angle $\displaystyle \theta$ whose sine equals $\displaystyle \frac{1}{2}$.

    Also, think about the unit circle...where is the sine function positive? You are only going to have two answers on the interval $\displaystyle [0,2\pi)$

    Sorry. Really, really sorry. I posted the wrong question.

    It's suppose to be:
    Find all θ in the interval [0,2) that satisfy the equation: $\displaystyle \sin {\theta} - \sin {\theta} \cot {\theta} = 0$
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