Results 1 to 10 of 10

Math Help - trigonometry

  1. #1
    sanya.batra
    Guest

    Unhappy trigonometry

    if A and B are acute angles and sinA=cosB,prove that A+B=90degrees
    plz help me
    Follow Math Help Forum on Facebook and Google+

  2. #2
    TD!
    TD! is offline
    Senior Member
    Joined
    Jan 2006
    From
    Brussels, Belgium
    Posts
    405
    Thanks
    3
    sin(a) = cos(b)
    sin(a) = sin(pi/2-b)

    a = pi/2-b <=> a+b = pi/2
    OR
    a = pi-(pi/2-b) <=> a = pi/2+b <=> a-b = pi/2

    If a and b are positive and acute, the bold answer is the only one remaining.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2006
    Posts
    3
    Please see attached I hope this makes sense.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Quick's Avatar
    Joined
    May 2006
    From
    New England
    Posts
    1,024
    Quote Originally Posted by zanyzanny View Post
    Please see attached I hope this makes sense.
    It does but it's worded pretty poorly...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2006
    Posts
    3
    Quote Originally Posted by Quick View Post
    It does but it's worded pretty poorly...
    I was trying to do it too quickly, sorry.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zanyzanny View Post
    Please see attached I hope this makes sense.
    Please try to avoid the use of proprietary file formats in attachments,
    not everybody can read them in their native application which can result
    in some unpleasant effects.

    I would usually favour turning anything less than about 1 page into
    a graphics format. I would recommend .png, but this site imposes a size
    limit on .png files so in practice a high quality .jpg seems to work best.

    RonL
    Attached Thumbnails Attached Thumbnails trigonometry-gash.jpg  
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2006
    Posts
    3
    Wow I have no idea what you just said or how you did that!
    It looks good though.
    Sorry I was just trying to be helpful. I don't have much idea about formats and stuff like that I am mostly interested in the maths
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Basically just do it in Paint. It gives you the option to save as a png file or a jpg file when you do Save As.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,740
    Thanks
    645
    Hello, sanya.batra!

    Here's a roundabout approach . . .


    Of A and B are acute angles and sin A = cos B,
    prove that: A + B = 90°

    We are given: .cos B .= .sin A . [1]

    Square both sides: .cos²B .= .sin²A

    Subtract from 1: .1 - cos²B .= .1 - sin²A

    And we have: .sin²B .= .cos²A

    Since A and B are acute: .sin B = cos A . [2]


    Now consider: .sin(A + B)

    . . . . . . . . . We have: .sin(A + B) .= .sin(A)·cos(B) + sin(B)·cos(A)
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    Substitute [1] and [2]: .sin(A + B) .= .sinA·sin(A) + cos(A)·cos(A)

    Hence: .sin(A + B) .= .sin²A + cos²A . . sin(A + B) .= .1


    Therefore: .A + B .= .90°

    (Recall that A and B are both acute angles.)

    Follow Math Help Forum on Facebook and Google+

  10. #10
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by zanyzanny View Post
    Wow I have no idea what you just said or how you did that!
    It looks good though.
    Sorry I was just trying to be helpful. I don't have much idea about formats and stuff like that I am mostly interested in the maths
    Produce the diagrams and text in any application you like.

    Display them on the screen, then alt-PrintScreen will capture
    the active window to the system clipboard. Open a graphics
    application and paste, or paste-as-new to paste the clipboard
    image into the application, crop to include only what you want
    in the final image, then resize and save in favourite format.

    Upload saved image file just like any other file and its done.

    RonL
    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, 12:03 PM
  2. How To Do Trigonometry For This...?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 10th 2009, 05:56 PM
  3. How To Do This Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 3rd 2009, 01:55 AM
  4. trigonometry
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 31st 2008, 08:06 PM
  5. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 18th 2008, 04:40 PM

Search Tags


/mathhelpforum @mathhelpforum