1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Express tan(2x) in terms of sin(x) alone.

  1. Mar 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Express tan(2x) in terms of sin(x) alone.

    assuming: pi < x < 3pi/2

    2. Relevant equations

    Trig identities

    3. The attempt at a solution

    sin2x/cos2x

    switched for double angle equations;

    (2sinx*cosx)/((cosx)^2 - (sinx)^2)

    then wherever i go with it, it leads nowhere.
     
  2. jcsd
  3. Mar 20, 2008 #2
    [tex]\cos x=\sqrt{1-\sin^2 x}[/tex]

    [tex]\cos{2x}=1-2\sin^2 x[/tex]
     
  4. Sep 25, 2009 #3
    Well tan2x=Sin2x/Cos2x then
    Sin2x= Tan2x*Cos2x but note that Cos^2(2x)=1/Sec^2(2x) using sec^2(2x)=1+ tan^2(2x) we then get
    Sin2x=Tan2x/Sqrt(1+tan^2(2x)) this is all ok but sin2x=2sinxcosx so you need to do the same for cos2x and find cosx in terms of tan2x thus replace it into the expression above.
    I hope this helps.
     
  5. Sep 25, 2009 #4
    Yes I just realised that you can get nicer expression if you see that

    cos2x=1/Sqrt(1+tan^2(2x)) then cos2x=1-2sin^2(x)
    hence
    1-2sin^2(x)=1/(Sqrt(1+tan^2(2x)))
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Express tan(2x) in terms of sin(x) alone.
  1. Calculus(f(x)= tan(2x) (Replies: 5)

  2. Fourier (sin(2x)*x^2) (Replies: 9)

Loading...