Results 1 to 3 of 3

Math Help - Prove sinA+sinB>sinC>|sinA-sinB|

  1. #1
    Senior Member
    Joined
    Jan 2009
    Posts
    290

    Prove sinA+sinB>sinC>|sinA-sinB|

    If A+B+C=180, then prove \sin A+\sin B>\sin C>|\sin A-\sin B|

    I can prove \sin A+\sin B>\sin C by

    2\sin \frac{A+B}{2}\cos \frac{A-B}{2}>2\sin \frac{C}{2}\cos \frac{C}{2}

    \cos \frac{A-B}{2}>\cos \frac{A+B}{2}

    \cos \frac{A-B}{2}-\cos \frac{A+B}{2}>0

    2\sin A\sin B>0

    Since sin is positive from 0 to 180, \sin A\sin B>0 and \sin A+\sin B>\sin C

    I can't prove the next part. Help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    To prove sinC> sin(A-B)

    2sin(C/2)cos(C/2) > 2cos([A+B)/2]*sin[(A-B)/2]

    sin[(A+B)/2] > sin[A-B)/2]

    A+B and A-B are less than 180 degrees.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    To prove sinC> sin(A-B)

    2sin(C/2)cos(C/2) > 2cos([A+B)/2]*sin[(A-B)/2]

    sin[(A+B)/2] > sin[A-B)/2]

    A+B and A-B are less than 180 degrees.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find Exact Value of SinB
    Posted in the Trigonometry Forum
    Replies: 17
    Last Post: October 8th 2011, 02:32 PM
  2. |sinA - sinB| < |A-B|
    Posted in the Trigonometry Forum
    Replies: 12
    Last Post: August 6th 2011, 12:23 PM
  3. Sina alpha, Cosine beta...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 22nd 2010, 06:26 PM
  4. sina*cosa=4/7 , a=?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 2nd 2010, 11:50 PM
  5. tan(A-B)/tan(A) + (sinC)^2/(sinA)^2=1
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 28th 2009, 01:29 AM

Search Tags


/mathhelpforum @mathhelpforum