Results 1 to 3 of 3

Math Help - Help

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    3

    Help

    Help me, please.
    arcsin (sin(9Pi/5) = ?
    arctg (tg (7Pi/5) = ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2008
    From
    France
    Posts
    1,458
    Quote Originally Posted by Netochka View Post
    Help me, please.
    arcsin (sin(9Pi/5) = ?
    arctg (tg (7Pi/5) = ?
    Hi

    If you can find k integer so that -\frac{\pi}{2} \leq \theta + 2k \pi \leq \frac{\pi}{2} then Arcsin(\sin(\theta)) = \theta + 2k \pi

    If not then exist n integer so that -\frac{\pi}{2} \leq -\theta + (2n+1) \pi \leq \frac{\pi}{2} and then Arcsin(\sin(\theta)) = -\theta + (2n+1) \pi

    For instance
    For \theta = \frac{9\pi}{5}
    \theta -2 \pi = -\frac{\pi}{5} and -\frac{\pi}{2} \leq -\frac{\pi}{5} \leq \frac{\pi}{2} then Arcsin(\sin(\frac{9\pi}{5})) = -\frac{\pi}{5}

    For \theta = \frac{7\pi}{5}
    \theta -2 \pi = -\frac{3\pi}{5} and -\frac{3\pi}{5} < -\frac{\pi}{2}
    -\theta + \pi = -\frac{2\pi}{5}
    -\frac{\pi}{2} \leq -\frac{2\pi}{5} \leq \frac{\pi}{2} then
    Arcsin(\sin(\frac{7\pi}{5})) = -\frac{2\pi}{5}


    For Arctan it is more simple
    Arctan(\tan(\theta)) = \theta + k \pi so that -\frac{\pi}{2} < \theta + k \pi < \frac{\pi}{2}
    Arctan(\tan(\frac{7\pi}{5})) = \frac{2\pi}{5}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2008
    Posts
    3
    Thank you very much
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum