Results 1 to 9 of 9

Math Help - Solving another simple trig. equation...

  1. #1
    Junior Member jonnygill's Avatar
    Joined
    Feb 2011
    Posts
    57

    Solving another simple trig. equation...

    The equation is...

    1+cot^2\Theta-3csc\Theta=0

    I tried substituting \dfrac{cos^2\Theta}{sin^2\Theta} for cot^2\Theta and replaced csc\Theta with \dfrac{1}{sin\Theta}.

    I was left with...

    \dfrac{cos^2\Theta}{sin^2\Theta}-\dfrac{3}{sin\Theta}=-1

    And now i'm pretty confused. I tried cross multiplying and getting a common denominator, but that just kept me going in circles. Which is when i realized i was doing something wrong.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    Good thus far. Now multiply through by \sin^2 \theta (which happens to be the LCD of sin^2(x), sin(x) and 1)

    \cos^2\theta- 3\sin \theta +1 = 0

    Now you can sub in \cos^2 \theta = 1- \sin^2 \theta

    1-\sin^2 \theta - 3\sin \theta +1 = 0 \implies \sin^2 \theta + 3\sin \theta -2 = 0

    (I moved everything to the other side because I prefer dealing with positive values of a)

    Use the quadratic formula to solve for \sin \theta and then \theta
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    another way:

    use the identity: \csc^2(x)-\cot^2(x)=1

    \therefore 1+\cot^2(x)=\csc^2(x)

    then:

    1+\cot^2(\theta)-3\csc(\theta)=0 \implies \csc^2(\theta)=3\csc(\theta)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member jonnygill's Avatar
    Joined
    Feb 2011
    Posts
    57
    oh, cool.

    ok, so i plugged into the quad. equation the numbers 1, 3, and -2 respectively.

    when i used the positive square root of 17 i got an answer of about 34.1633 degrees.

    However, when i used the negative square root of 17 i got an error on my calculator. does this simply mean there is only one answer?

    thanks!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    -1
    e^(i*pi)'s Avatar
    Joined
    Feb 2009
    From
    West Midlands, England
    Posts
    3,053
    Thanks
    1
    You won't get an answer because it's an extraneous solution since the range is -1 \leq \cos \theta \leq 1. You can discard that answer that gave you an error.

    I suspect there is more than one solution of 0 < x < 360

    what they are I don't know since it's half 2 in the morning and I should be in bed!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member jonnygill's Avatar
    Joined
    Feb 2011
    Posts
    57
    thank you.

    if there is another solution with 0 < x < 360 i do not know what it is.

    if anyone knows that there is another solution, how to find it, and is willing to show me i would be very grateful.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member jonnygill's Avatar
    Joined
    Feb 2011
    Posts
    57
    Quote Originally Posted by harish21 View Post
    another way:

    use the identity: \csc^2(x)-\cot^2(x)=1

    \therefore 1+\cot^2(x)=\csc^2(x)

    then:

    1+\cot^2(\theta)-3\csc(\theta)=0 \implies \csc^2(\theta)=3\csc(\theta)

    thanks!

    but i can't use the quad. equation for the csc function right? so how would i solve csc^2(\theta)=3\csc(\theta)
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,569
    Thanks
    1428
    Sure you can...

    \displaystyle \csc^2{\theta} - 3\csc{\theta} = 0

    \displaystyle \csc{\theta}(\csc{\theta} - 3) = 0

    \displaystyle \csc{\theta} = 0 or \displaystyle \csc{\theta} - 3 = 0.

    Solve each for \displaystyle \theta...
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member jonnygill's Avatar
    Joined
    Feb 2011
    Posts
    57
    Quote Originally Posted by Prove It View Post
    Sure you can...

    \displaystyle \csc^2{\theta} - 3\csc{\theta} = 0

    \displaystyle \csc{\theta}(\csc{\theta} - 3) = 0

    \displaystyle \csc{\theta} = 0 or \displaystyle \csc{\theta} - 3 = 0.

    Solve each for \displaystyle \theta...
    cool!

    so i don't even need the quadratic equation for this problem.

    thanks!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple equation solving
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 18th 2011, 10:20 AM
  2. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  3. Simple equation solving
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 13th 2009, 01:14 PM
  4. Solving a simple equation
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 30th 2009, 08:23 PM
  5. solving a simple trig equation
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 5th 2006, 09:09 PM

Search Tags


/mathhelpforum @mathhelpforum