Results 1 to 10 of 10

Math Help - sine and cosine

  1. #1
    Member OnMyWayToBeAMathProffesor's Avatar
    Joined
    Sep 2006
    Posts
    157

    sine and cosine

    I am stuck on these two problems. I have absolutely no idea how to get them. any help would be greatly appreciated.

    1. 1-4sin^2xcos^2x<br />
    2. cos^22x-cos^2x=sin^2xtan^2x I just think you have to solve the identity

    the answer has to be simplified to a single term.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    I am stuck on these two problems. I have absolutely no idea how to get them. any help would be greatly appreciated.

    1. 1-4sin^2xcos^2x<br />

    For the 1st one

    1-4sin^2xcos^2x=1-(2 \sin(x) \cos(x))^2=1-\sin^2(2x)=\cos^{2}(2x)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
    Joined
    Sep 2006
    Posts
    157
    could you please explain this step.
    <br />
1-(2 \sin(x) \cos(x))^2=1-\sin^2(2x)=\cos^{2}(2x)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    could you please explain this step.
    <br />
1-(2 \sin(x) \cos(x))^2=1-\sin^2(2x)=\cos^{2}(2x)
    I used this identity \sin(2x)=2\sin(x) \cos(x)

    and this one

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

  5. #5
    Member OnMyWayToBeAMathProffesor's Avatar
    Joined
    Sep 2006
    Posts
    157
    Thanks a lot. makes sense now.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member OnMyWayToBeAMathProffesor's Avatar
    Joined
    Sep 2006
    Posts
    157
    any idea on the second one?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,408
    2nd one isn't an identity because it doesn't work for all values of x. For example, if we let x = \frac{\pi}{5}, then the left hand side is about -.559 while the right hand side is about .182.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member OnMyWayToBeAMathProffesor's Avatar
    Joined
    Sep 2006
    Posts
    157
    I apologize for the inconvenience but number 2 is NOT correct. these are the ones i meant to type in.

    2) cos(3x)=4cos^3x-3cosx

    3) cos^22x-cos^2x=sin^2x-sin^22x

    I would like to thank everybody who tried to help me. Once again I apologize. These are both identities. I did some work on number 2 but then I got stuck. I do not understand number 3.

    Thank You.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,408
    2. Use the double angle formula for cosine using 3x = 2x + x and convert all your sin terms into cos terms.

    3. Ignore the angles and just convert the cosine terms into sine terms.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78

    Check this thread

    http://www.mathhelpforum.com/math-he...ease-help.html

    This thread has the same questions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cosine and Sine Help
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 24th 2009, 08:15 PM
  2. cosine and sine
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: May 7th 2009, 07:14 AM
  3. Cosine/Sine
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 5th 2009, 06:10 PM
  4. Sum of sine and cosine
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 2nd 2008, 06:19 AM
  5. Cosine/Sine
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 25th 2006, 09:53 AM

Search Tags


/mathhelpforum @mathhelpforum