Results 1 to 3 of 3

Math Help - another easy trig problem...

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

    another easy trig problem...

    hello again!

    ok, so here's a problem where it asks to change the equation so that "only one trigonometric ratio is present."

    the equation is...

    sin\Theta=cos\Theta

    now, i'm only aware of one trig. identity that explains sin in terms of cos and it is called a half-angle identity.

    and it looks like this...

    sin\dfrac{\Theta}{2}=\pm\sqrt\dfrac{1-cos\Theta}{2}

    Is this the identity i would use so that only one trig. ratio is present?

    if so, could i just say...

    sin\Theta=\pm\sqrt\dfrac{1-cos2\Theta}{2}

    or maybe...

    sin\Theta=\pm2\sqrt\dfrac{1-cos\Theta}{2}
    Last edited by jonnygill; February 17th 2011 at 08:11 PM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Very good, but \sin^{2}(x) + \cos^{2}(x) = 1 should also be familiar and will lead to the same conclusion. Isn't is lovely that unique solutions don't care how you find them?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,923
    Thanks
    332
    Awards
    1
    Quote Originally Posted by jonnygill View Post
    hello again!

    ok, so here's a problem where it asks to change the equation so that "only one trigonometric ratio is present."

    the equation is...

    sin\Theta=cos\Theta

    now, i'm only aware of one trig. identity that explains sin in terms of cos and it is called a half-angle identity.

    and it looks like this...

    sin\dfrac{\Theta}{2}=\pm\sqrt\dfrac{1-cos\Theta}{2}

    Is this the identity i would use so that only one trig. ratio is present?

    if so, could i just say...

    sin\Theta=\pm\sqrt\dfrac{1-cos2\Theta}{2}

    or maybe...

    sin\Theta=\pm2\sqrt\dfrac{1-cos\Theta}{2}
    I think you are over-thinking this one. Take your original equation:
    \displaystyle sin( \theta ) = cos( \theta )

    What happens if you divide both sides by \displaystyle cos( \theta )?

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: February 9th 2013, 08:59 PM
  2. Another easy trig. problem...
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 17th 2011, 07:29 PM
  3. Easy trig problem
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 2nd 2010, 11:04 PM
  4. Easy trig function problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 18th 2010, 12:03 PM
  5. Easy trig simplification problem.
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 4th 2009, 02:15 PM

Search Tags


/mathhelpforum @mathhelpforum