Results 1 to 5 of 5

Math Help - Solve for θ over the given domain

  1. #1
    Junior Member
    Joined
    Jul 2008
    From
    Sydney, Australia
    Posts
    30

    Solve for θ over the given domain

    √3 sin 2θ = cos 2θ
    Domain: 0o ≤ θ ≤ 360o
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,706
    Thanks
    625
    Hello, sweetG!

    \sqrt{3}\sin2\theta \:=\:\cos2\theta\qquad 0^o \leq \theta \leq 360^o
    Divide by \sqrt{3}\cos2\theta\!:\;\;\frac{\sin2\theta}{\cos2  \theta} \:=\:\frac{1}{\sqrt{3}} \quad\Rightarrow\quad \tan2\theta \:=\:\frac{1}{\sqrt{3}}


    Then: . 2\theta\;=\;30^o,\: 210^o,\: 390^o,\: 570^o


    Therefore: . \theta \;=\;15^o,\:105^o,\:195^o,\:285^o

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2008
    From
    Sydney, Australia
    Posts
    30
    Thanks so much Soroban that really helped a lot
    But I've forgotten how to do one thing......how did you get the answers that come after 30 degrees i.e. 210, 390 and 570 degrees. I've forgotten how do these types of questions
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Sep 2007
    Posts
    528
    Awards
    1
    Quote Originally Posted by sweetG View Post
    Thanks so much Soroban that really helped a lot
    But I've forgotten how to do one thing......how did you get the answers that come after 30 degrees i.e. 210, 390 and 570 degrees. I've forgotten how do these types of questions
    The \tan \theta function has a period of 180^{\circ} hence when you add 180^{\circ}, you get the value for \theta which will satisfy your equation. There are infinite solution hence questions usually provide a range (in this case 0^o \leq \theta \leq 360^o).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2008
    From
    Sydney, Australia
    Posts
    30

    Smile

    Thanks Soroban and Air that really helped and now I'm a lot more clearer on how to do these types of questions
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Converting from the S domain to the Z domain
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: February 24th 2011, 10:15 PM
  2. need to solve summation equation to solve sum(x2)
    Posted in the Statistics Forum
    Replies: 2
    Last Post: July 16th 2010, 10:29 PM
  3. Replies: 6
    Last Post: February 12th 2010, 01:06 PM
  4. Replies: 6
    Last Post: September 16th 2009, 06:25 AM
  5. find the domain and solve polynomial
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 1st 2008, 10:41 PM

Search Tags


/mathhelpforum @mathhelpforum