Results 1 to 4 of 4

Math Help - Trigonomtery Angles: Compound Angle Formulas

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    Trigonomtery Angles: Compound Angle Formulas

    What would be the formula for
    -cos(A-B) = ?
    -cos(A+B) = ?
    -sin(A-B) = ?
    -sin(A+B) = ?

    I don't understand what happens with a negative in front of cos and sin, that's my point..

    For example:
    cos(11pi/12) ends up being -cos(pi/4-pi/6)
    cos (17pi/12) ends up being -cos(pi/4-pi/6) also
    [correct me if i am wrong]
    and then, if i used the formula -cos(A-B) = -cosAcosB+sinAsinB
    the formula on the right side of both questions are the same, yet if i leave the same formula on the right for both equations (since the left is the same) then i don't get the right answer.. one of them needs -cosAcosB-sinAsinB for the left and the other one needs -cosAcosB+sinAsinB in order to get the correct answer.

    this is what I dont understand, how do you know which one it is?
    Last edited by skeske1234; March 25th 2009 at 02:47 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576
    Quote Originally Posted by skeske1234 View Post
    What would be the formula for
    -cos(A-B) = ?
    -cos(A+B) = ?
    -sin(A-B) = ?
    -sin(A+B) = ?

    I don't understand what happens with a negative in front of cos and sin, that's my point..
    Expand the \cos{(A - B)} (say) as you usually would, then switch all the signs.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2008
    Posts
    425
    Quote Originally Posted by Prove It View Post
    Expand the \cos{(A - B)} (say) as you usually would, then switch all the signs.
    What do you mean..? I don't follow..
    Can you try explaining it using my example please and thank you
    cos(11pi/12) and cos(17pi/12)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576
    Quote Originally Posted by skeske1234 View Post
    What do you mean..? I don't follow..
    Can you try explaining it using my example please and thank you
    cos(11pi/12) and cos(17pi/12)
    \cos{\frac{17\pi}{12}} = \cos{\left(\frac{9\pi}{12} + \frac{8\pi}{12}\right)} = \cos{\left(\frac{3\pi}{4} + \frac{2\pi}{3}\right)}

    \cos{\left(\frac{3\pi}{4} + \frac{2\pi}{3}\right)} = \cos{\left(\frac{3\pi}{4}\right)}\cos{\left(\frac{  2\pi}{3}\right)} - \sin{\left(\frac{3\pi}{4}\right)}\sin{\left(\frac{  2\pi}{3}\right)}

    Can you go from here?


    For your example re what happens when there's a negative out the front...

    -\cos{\left(\frac{3\pi}{4} + \frac{2\pi}{3}\right)} = -\left[\cos{\left(\frac{3\pi}{4}\right)}\cos{\left(\frac{  2\pi}{3}\right)} - \sin{\left(\frac{3\pi}{4}\right)}\sin{\left(\frac{  2\pi}{3}\right)}\right]

    Just use the distributive law...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Compound Angle Formulas.
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 25th 2009, 10:48 PM
  2. Compound Angle Formulas
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 29th 2009, 09:41 AM
  3. Compound Angle Formulas
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: March 28th 2009, 06:08 PM
  4. compound angle formulas
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 9th 2008, 10:19 AM
  5. Replies: 1
    Last Post: November 14th 2007, 09:30 PM

Search Tags


/mathhelpforum @mathhelpforum