Results 1 to 10 of 10
Like Tree4Thanks
  • 1 Post By HallsofIvy
  • 1 Post By MarkFL
  • 1 Post By HallsofIvy
  • 1 Post By harish21

Math Help - Eliminating theta

  1. #1
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Eliminating theta

    I have the two equations:

    1) x + y = qsin(theta)

    2) z = rcos(theta)


    The question is eliminate theta and solve for q in terms of x, y, z, and r.

    I'm not sure what eliminating theta means, but I have:

    arcsin((x+y)/q) = theta

    and I substituted that into my top equation. I have no clue on what I should do now.

    Also,I don't understand how I can solve for q in terms of z and r when q isn't in the equation with z and r.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,454
    Thanks
    1868

    Re: Eliminating theta

    How about using the fact that sin^2(\theta)+ cos^2(\theta)= 1?
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Eliminating theta

    Perhaps an easier approach would be to write your equations as:

    (1) \frac{x+y}{q}=\sin\theta

    (2) \frac{z}{r}=\cos\theta

    Now square both equations and add, and the right side will be an identity which will eliminate \theta.
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Eliminating theta

    Should I have sin^2(arcsin(x+y)/q) + cos^2(arccos(z/r)) =1?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Eliminating theta

    Nevermind my last post
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Eliminating theta

    I have q^2 = ((x+y)^2)/(1-(z/r)^2)

    Sorry, I don't know how to make it look neater than that.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,454
    Thanks
    1868

    Re: Eliminating theta

    Well, you could write the left side as \frac{(x+ y)^3}{1- \frac{z^2}{r^2}}= \frac{r^2(x+ y)^2}{r^2- z^2}, multiplying both numerator and denominator by r^2. And, of course, since you are asked to find q, you still need to take the square root of both sides.
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Eliminating theta

    Before reading your reply I got:

    q=\sqrt{\frac{(x+y)^2}{1-\frac{z^2}{r^2}}

    Your method gets rid of the fraction in the denominator so:

    q=\sqrt{\frac{r^2(x+ y)^2}{r^2- z^2}}

    Correct?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10

    Re: Eliminating theta

    Quote Originally Posted by amthomasjr View Post
    Before reading your reply I got:

    q=\sqrt{\frac{(x+y)^2}{1-\frac{z^2}{r^2}}

    Your method gets rid of the fraction in the denominator so:

    q=\sqrt{\frac{r^2(x+ y)^2}{r^2- z^2}}

    Correct?
    that looks right.. it can be further simplified as q=\frac{r(x+ y)}{\sqrt{r^2- z^2}}
    Thanks from amthomasjr
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Sep 2011
    From
    San Antonio, TX
    Posts
    45

    Re: Eliminating theta

    Thank you all.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: April 29th 2010, 10:24 AM
  2. Replies: 2
    Last Post: March 29th 2010, 07:38 AM
  3. Replies: 3
    Last Post: February 6th 2009, 04:19 PM
  4. Replies: 1
    Last Post: January 23rd 2009, 10:53 AM
  5. Solve sin4(theta) = cos2(theta)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 8th 2008, 11:23 AM

Search Tags


/mathhelpforum @mathhelpforum