Results 1 to 2 of 2

Math Help - trigonometry

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    1

    trigonometry

    cosa-sina=0
    or
    cosa+sina=1

    how to find a?
    the only why which i came out with is to square, but i think if i do so i'll lose (not always but sometimes) several meanings of a..
    i hope you understood what i was trying to say
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2008
    Posts
    135

    Solution

    cosa-sina=0
    or
    cosa+sina=1

    I was thinking you could square the bottom equation to get:
    (cosa)^2 + 2cosasina + (sina)^2 = 1

    Group terms to get:
    (cosa)^2 + (sina)^2 + 2cosasina = 1

    The first two terms form the identity:
    (cosa)^2 + (sina)^2 = 1

    So, using substitution:
    1 + 2cosasina = 1
    which reduces to:
    2cosasina = 0

    Now, the above forms the double angle identity:
    sin2a = 2sinacosa

    So, using substitution:
    sin2a = 0

    Now, we have to figure what angles would cause sin2a = 0:
    0, +/- Pi/2, +/- Pi, +/- 3Pi/2,...

    Normally, these angles would cause sin to equal 1 or -1, but since it is 2 times the angle it causes sin2a to equal zero.

    a is written of the form:

    a = +/- (n*Pi/2) for some n = 0, +/-1, +/-2,...

    Part 2.

    Do the same for the first equation:
    (cosa)^2 - 2cosasina + (sina)^2 = 0

    Again, use the identity:
    (cosa)^2 + (sina)^2 = 1

    Substitute:
    1-2cosasina = 0

    Add 2cosasina to both sides:
    2cosasina = 1

    Use the double angle formula:
    sin2a =1

    Now, we have to find what values will cause sin2a to equal 1:
    Pi/4, 5Pi/4, 9Pi/4...
    This is true because when the angle is multiplied by 2, it will be of the form n*Pi/2, which causes sin to equal 1 only when it is on the positive y axis. Otherwise, if 3Pi/4 were included, for example, it would cause sin2a to equal -1 because it would be the negative y axis.

    So, a is expressed as:

    a = n*Pi/4 for some n = 1,5,9,...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry to Memorize, and Trigonometry to Derive
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: August 21st 2013, 01:03 PM
  2. How To Do Trigonometry For This...?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 10th 2009, 06:56 PM
  3. How To Do This Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 3rd 2009, 02:55 AM
  4. trigonometry
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 31st 2008, 09:06 PM
  5. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 18th 2008, 05:40 PM

Search Tags


/mathhelpforum @mathhelpforum