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Math Help - Homework Help!! exact value, -pi < θ ≤ pi

  1. #1
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    Homework Help!! exact value, -pi < θ ≤ pi

    Hi All,

    Could somebody please explain (step by step) how to find the exact value of sinx= -1/√2 when -pi < θ ≤ pi? Been trying to google but the only example is between 0 < θ ≤ 2pi..

    Many thanks
    Last edited by jjcp; March 31st 2013 at 01:35 AM.
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  2. #2
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    Get the solutions for the easy region, then add multiples of 2pi until you have all the solutions in the region you are given.
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    \text{Disregard the minus sign temporarily and put} \\  \\ sin^{-1} \frac{1}{\sqrt{2}} \\ \\ \text{in your calculator, this will give you the reference angle of 45 or} \ \frac{\pi}{4}  \\ \\   \text{The sine is negative in 3rd and 4th quadrants so your 2 solutions will be} \\  \\ - \pi \ + \ \frac{\pi}{4} \ = \ - \frac{3 \pi}{4} \\ \\ and \\ \\ - \frac{\pi}{4}
    Last edited by agentmulder; March 31st 2013 at 05:06 AM.
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    Quote Originally Posted by agentmulder View Post
    \text{Disregard the minus sign temporarily and put} \\  \\ sin^{-1} \frac{1}{\sqrt{2}} \\ \\ \text{in your calculator, this will give you the reference angle of 45 or} \ \frac{\pi}{4}  \\ \\   \text{The sine is negative in 3rd and 4th quadrants so your 2 solutions will be} \\  \\ - \pi \ + \ \frac{\pi}{4} \ = \ -3 \frac{\pi}{4} \\ \\ and \\ \\ - \frac{\pi}{4}
    I'm sure you mean \displaystyle -\frac{3\pi}{4}...
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    Yes, i guess the way i wrote it the fraction looked like a mixed number, i edited the post.
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    Keep in mind that the sin(-x) = -sinx

    Howard Heller
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    Quote Originally Posted by IMTinstructor View Post
    Keep in mind that the sin(-x) = -sinx

    Howard Heller
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    Anyone stupid enough to fall for you scam deserves the outcome.
    I can find no entry for you at MathGenealogy Project

    So what equips you to tutor?
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    Re: Homework Help!! exact value, -pi < θ ≤ pi

    What equips me to tutor? First of all, equips is not english to you must be from another country. I though am from the United States. Lets see... Math major, expert in math, actuary science major, mba, etc etc.
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