Results 1 to 5 of 5

Math Help - Simple (I think) trigonometric equation

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    3

    Simple (I think) trigonometric equation

    Well it's been a while since I exercised my trig brain so I'm in need of a bit of help with this one. The problem I'm trying to solve is related to this: Problem 202 - Project Euler and part of it involves solving an equation that might look something like this:

    \sin{(\frac{2\pi}{3}-x)}=1.4 \sin{(x)}

    I actually know what the solution is to this one (by numerical solving) by I don't know how to achieve it algebraically. Any hints anyone could give would be great.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by spuz View Post
    Well it's been a while since I exercised my trig brain so I'm in need of a bit of help with this one. The problem I'm trying to solve is related to this: Problem 202 - Project Euler and part of it involves solving an equation that might look something like this:

    \sin{(\frac{2\pi}{3}-x)}=1.4 \sin{(x)}

    I actually know what the solution is to this one (by numerical solving) by I don't know how to achieve it algebraically. Any hints anyone could give would be great.

    Thanks
    i don't think pure algebra can get you very far with this. by the addition formula for sine, we have:

    \sin \bigg( \frac {2 \pi}3 - x\bigg) = \frac 75 \sin x

    \Rightarrow \sin \frac {2 \pi}3 \cos x - \sin x \cos \frac {2 \pi}3 = \frac 75 \sin x

    this simplifies to:

    \frac {\sqrt{3}}2 \cos x - \frac 9{10} \sin x = 0

    and the algebra is not worth it from there. continue numerically
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    3
    Hmm, very interesting. When I typed this into quickmath's equation solver it managed to find an exact solution algebraically though I imagine it must have been through many complicated steps if you say it's not worth the trouble. Oh well, it looks like I may be going about this problem in the wrong way....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Dec 2007
    From
    Anchorage, AK
    Posts
    276
    Continuing from where Jhevon left off, we have \frac{\sqrt{3}}{2}\cos{x}-\frac{9}{10}\sin{x}=0
    \frac{\sqrt{3}}{2}\cos{x}=\frac{9}{10}\sin{x}
    \sin{x}=\frac{5\sqrt{3}}{9}\cos{x}
    \frac{\sin{x}}{\cos{x}}=\frac{5\sqrt{3}}{9}
    \tan{x}=\frac{5\sqrt{3}}{9}
    x=\arctan\frac{5\sqrt{3}}{9}

    I don't see that you can simplify any further than that, except numerically.

    --Kevin C.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    3
    Thanks very much TwistedOne151, that's exactly what I needed. The solution of that equation matches the value of x I found numerically so that's great.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help to solve simple trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: September 14th 2010, 06:40 AM
  2. Simple trigonometric equation can you help?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 26th 2009, 03:07 PM
  3. [SOLVED] simple trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: February 10th 2009, 03:23 PM
  4. simple trigonometric equation help
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 24th 2008, 03:28 PM
  5. simple trigonometric equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 27th 2006, 10:58 AM

Search Tags


/mathhelpforum @mathhelpforum