Results 1 to 6 of 6

Math Help - Eliminating the parameter when sin and cos are involved.

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    14

    Eliminating the parameter when sin and cos are involved.

    Hello! I've just started Calculus in college but my Trig class in high-school was a joke and I didn't get much out of it (mostly my fault) so I thought this question would belong in the pre-university trig forum. Please correct me if I'm wrong.


    a) Eliminate the parameter to find a Cartesian equation of the curve.

    x = sin1/2theta , y = cos1/2theta , -pi <= theta <= pi

    (sorry I'm also a noob on writing math nicely on a computer, a link to a tutorial would be nice)

    I thought about using the rule of sin^2theta + cos^2theta = 1 but I'm not sure how to get it into that form algebraically or even what the hints are that I should do that...?

    Thanks
    Last edited by buddyp450; January 24th 2010 at 01:06 PM. Reason: added domain, fixed noob mistake
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    Quote Originally Posted by buddyp450 View Post
    Hello! I've just started Calculus in college but my Trig class in high-school was a joke and I didn't get much out of it (mostly my fault) so I thought this question would belong in the pre-university trig forum. Please correct me if I'm wrong.


    a) Eliminate the parameter to find a Cartesian equation of the curve.

    x = sin1/2theta , y = sin1/2theta , -pi <= theta <= pi

    (sorry I'm also a noob on writing math nicely on a computer, a link to a tutorial would be nice)

    I thought about using the rule of sin^2theta + cos^2theta = 1 but I'm not sure how to get it into that form algebraically or even what the hints are that I should do that...?

    Thanks
    note that y = x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    14
    fixed
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,698
    Thanks
    454
    you have the right idea ...

    x^2 = \sin^2\left(\frac{\theta}{2}\right) <br />

    y^2 = \cos^2\left(\frac{\theta}{2}\right)

    x^2+y^2 = 1

    the equation of the unit circle ... however, since y =  \cos\left(\frac{\theta}{2}\right) > 0 for -\pi \le \theta \le \pi

    y = \sqrt{1-x^2}

    the upper semicircle of radius 1.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    14
    Am I correct in saying that

    y = \sqrt{1-x^2}

    is the same as

    <br /> <br />
y = \sqrt{1-\sin^2\left(\frac{\theta}{2}\right)}

    and that the latter would be the proper Cartesian equation of the curve?

    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by buddyp450 View Post
    Am I correct in saying that

    y = \sqrt{1-x^2}

    is the same as

    <br /> <br />
y = \sqrt{1-\sin^2\left(\frac{\theta}{2}\right)}

    and that the latter would be the proper Cartesian equation of the curve?
    Why would you do this? Especially since the point is to elminate the parameter!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find loci (parameter involved)
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 17th 2011, 03:35 AM
  2. hypothesis testing: parameter 0 against parameter positive.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 10th 2011, 02:49 PM
  3. eliminating parameter to find cartesian eq.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 29th 2010, 02:08 AM
  4. Eliminating the parameter in parametric equations?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: November 28th 2009, 01:31 PM
  5. eliminating the parameter to obtain an x-y equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 26th 2009, 01:25 AM

Search Tags


/mathhelpforum @mathhelpforum