Results 1 to 7 of 7

Math Help - Trig problem

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    11

    Trig problem

    Help I have spent about 3 days on this one, where I get lost is with the final part of the question



    Use standard identities to express sin(3theta+(sqrt/4) in terms of sin theta and cos theta.



    My tutor has explained it, but in terms of asuming that I know all the steps that he missed (a bit like here is a matrix, here is the determinate and missing the bits between)
    Thanks

    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 dazza67 View Post
    Help I have spent about 3 days on this one, where I get lost is with the final part of the question



    Use standard identities to express sin(3theta+(sqrt/4) in terms of sin theta and cos theta.



    My tutor has explained it, but in terms of asuming that I know all the steps that he missed (a bit like here is a matrix, here is the determinate and missing the bits between)
    Thanks
    If you post the solution you have and flag the steps you don't get, someone will fill in the gaps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    11
    Thanks Mr. Fantastic. This is about where I got to

    [quote] Use standard identities to express sin(3θ+(π/4) in terms of sin θ and cos θ
    as best as I get
    sin
    (3θ+(π/4))
    sin(A+B)=sinAcosB+cosAsinB
    the answer that I was given by a colleague
    Ans = ((2sin θ cos θ)cos θ)+(sin θ(1-2 sin θ)) cos π/4 + sin π/4 ((1-2 sin θ) cos θ) - ((2 sin θ cos θ) sin θ

    so here is where my problem is.

    I end up with sin(3θ)cos(π/4)+cos(3θ)sin(π/4)
    I need to know that if I am wrong, why and if he is right, how did he get there from where I am or am I just completely on the wrong path
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
    Hello Dazza. You are not wrong. You just need to expand more:

    You got: sin(3\theta)cos\frac{\pi}{4} + cos(3\theta)sin\frac{\pi}{4}

    Now make it: sin(2\theta+ \theta)cos\frac{\pi}{4} + cos(2\theta+\theta)sin\frac{\pi}{4}

    Expand that using the sum-difference formulas (i.e. sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB)
    Then expand the double angles.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2008
    Posts
    11
    Quote Originally Posted by Gusbob View Post
    Hello Dazza. You are not wrong. You just need to expand more:

    You got: sin(3\theta)cos\frac{\pi}{4} + cos(3\theta)sin\frac{\pi}{4}

    Now make it: sin(2\theta+ \theta)cos\frac{\pi}{4} + cos(2\theta+\theta)sin\frac{\pi}{4}

    Expand that using the sum-difference formulas (i.e. sin(A+B) = sinAcosB + cosAsinB, cos(A+B) = cosAcosB - sinAsinB)
    Then expand the double angles.
    Thanks for that, next dumb one,expand the double angles??
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87
     sin(2\theta) = 2sin(\theta)cos(\theta)

     cos(2\theta) =
    cos^2(\theta) - sin^2(\theta)
    or  2cos^2(\theta)-1
    or 1-2sin^2(\theta)
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    May 2008
    Posts
    11
    Thanks for all of your help Gusbob. I will now follow the flow and work thru the rest of the problems, you have very much filled in a couple of missing steps, once again thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig word problem - solving a trig equation.
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: March 14th 2011, 07:07 AM
  2. Replies: 3
    Last Post: January 2nd 2011, 08:20 PM
  3. trig problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: May 13th 2009, 06:28 PM
  4. trig problem
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 10th 2008, 04:23 AM
  5. trig problem
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: April 1st 2008, 02:16 AM

Search Tags


/mathhelpforum @mathhelpforum