Results 1 to 8 of 8

Math Help - Trigonometry Reduction Identity

  1. #1
    Newbie
    Joined
    Jul 2009
    Posts
    19

    Trigonometry Reduction Identity

    y = -sin x - cos x
    It says to use the reduction identity to graph each equation.
    I have absolutely no clue how to do this. I recall my teacher saying he doesn't like to use the reduction identity given in the book so he changes the form to m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x). Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jul 2009
    Posts
    1
    y=-senx-cosx
    y=-(senx+cosx)
    y=-sqrt(2){[(sqrt(2).senx)/2]+[(sqrt(2).cosx)/2]}
    y=-sqrt(2).sen(45+x)
    you will have a function that ranges from -sqrt(2) to sqrt(2);translated to the left by 45 degrees and being the reflex of the function y=sqrt(2).sen(45+x)
    hope it helps
    =)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2009
    Posts
    397
    Quote Originally Posted by hellojellojw View Post
    m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x).
    Do you know how to expand sin (a + b) ?

    Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.
    Compare the coefficients of m*sin(x + y) and (-sin x - cos x)
    Last edited by songoku; July 22nd 2009 at 08:14 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2009
    Posts
    19
    Quote Originally Posted by songoku View Post
    Do you know how to expand sin (a + b) ?



    Compare the coefficients of m*sin(x + y) and (-sin x - cos x)
    Yes I know the addition laws.

    The most I'm confused about is going from this msin(x)cos(y) + mcos(y)sin(x)
    to mcosy = -1 and msiny = -1.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Jul 2009
    Posts
    397
    Quote Originally Posted by hellojellojw View Post
    m*sin(x + y) and then use angle addition formula to get msin(x)cos(y) + mcos(y)sin(x). Then he states mcosy = -1 and msiny = -1. How did he get this? Because I have no clue how.
    y = - sin x - cos x
    = m*sin ( x + y )
    = msin(x)cos(y) + mcos(y)sin(x)

    Then, - sin x - cos x = msin(x)cos(y) + mcos(y)sin(x)

    Compare the left and right side of the equation
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Jul 2009
    Posts
    19
    Quote Originally Posted by songoku View Post
    y = - sin x - cos x
    = m*sin ( x + y )
    = msin(x)cos(y) + mcos(y)sin(x)

    Then, - sin x - cos x = msin(x)cos(y) + mcos(y)sin(x)

    Compare the left and right side of the equation
    ahh I see now I think.
    I just set -sinx = msinxcosy and got mcosy = -1.
    Thanks.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2009
    Posts
    19
    Oh yeah and one more quick question. How is
    -sin x - cos x = m sin(x + y)
    Like how do you come up with that?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Jul 2009
    Posts
    397
    it's because we don't have any formulas for sin x + cos y.

    There are formulas for sin x + sin y, sin x - sin y, cos x + cos y, cos x - cos y, but not sin x + cos y

    So, we just set that sin x + cos x = m sin(x + y) in order to simplify it.
    You can also set sin x + cos x = m sin(x - y), or sin x + cos x = m cos(x + y), or sin x + cos x = m cos(x - y).
    The process will be different, but the final answer will be the same if you want to find the exact value of x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry identity proof
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: June 3rd 2010, 08:45 AM
  2. Trigonometry Identity
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 1st 2009, 05:12 AM
  3. Trigonometry Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 26th 2009, 03:31 PM
  4. Trigonometry quotient identity?
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 20th 2008, 07:04 PM
  5. Trigonometry Reduction Formula
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 4th 2008, 02:07 AM

Search Tags


/mathhelpforum @mathhelpforum