Results 1 to 5 of 5

Math Help - Double Angle

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    17

    Double Angle

    hi i am really struggling with these 2 questions and any help would be deeply appreciated.

    1. 2cos 2theta= 7 sintheta solve for 0<theta<2 pi, answer to one decimal

    2. prove that
    1 - tan squared theta / 1 + tan squared theta = cos 2 theata
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by brooksy View Post
    hi i am really struggling with these 2 questions and any help would be deeply appreciated.

    1. 2cos 2theta= 7 sintheta solve for 0<theta<2 pi, answer to one decimal

    2. prove that
    1 - tan squared theta / 1 + tan squared theta = cos 2 theata
    1. Substitute \cos (2 \theta) = 1 - 2 \sin^2 (\theta ) and re-arrange to get the quadratic equation 4 \sin^2 \theta + 7 \sin \theta - 2 = 0.
    Solve for \sin \theta and then solve for \theta.

    2. Work with the left hand side: Substitute \tan \theta = \frac{\sin \theta}{\cos \theta}. Multiply numerator and denominator by \cos^2 \theta. Simplify the numerator and denominator using standard identities to get the right hand side.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    17
    thanks for that but im still really struggling to get the final answer.
    for 1. i've got to 4sinsquared theta + 7 sin theta -2=0 do i then factorise or what.

    2.ive mulitplied by cos squared theta and got
    cos squared theta - sin squared theta / cos squared theta + sin squared theta. not sure what to do next
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by brooksy View Post
    thanks for that but im still really struggling to get the final answer.
    for 1. i've got to 4sinsquared theta + 7 sin theta -2=0 do i then factorise or what. Mr F says: Yes. Or use the quadratic formula to solve for {\color{red}sin \theta}. Only one of the solutions for {\color{red}sin \theta} will be valid.

    2.ive mulitplied by cos squared theta and got
    cos squared theta - sin squared theta / cos squared theta + sin squared theta. not sure what to do next Mr F says: Surely you're familar with the double angle formulae and the Pythagorean Identity.
    I doubt very much that 9 minutes (the time between post #2 and post #3) is sufficient time to engage with the questions using the suggestions I made in post #2.
    Last edited by mr fantastic; November 10th 2008 at 04:54 AM. Reason: Agreed with factorising.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2008
    Posts
    17
    thanks for the help Mr F
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplify the Expression (Double-Angle or Half-Angle)
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 3rd 2009, 04:38 PM
  2. More double angle and Half angle problems
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 21st 2009, 07:54 PM
  3. Half angle or double angle Identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: July 21st 2009, 06:20 PM
  4. Help with double angle and half angle formulas
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 20th 2009, 06:30 PM
  5. Replies: 2
    Last Post: February 15th 2007, 11:16 PM

Search Tags


/mathhelpforum @mathhelpforum