Results 1 to 6 of 6

Math Help - Double Angle ID issues, did my teacher grade wrong?

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    Double Angle ID issues, did my teacher grade wrong?

    If Sin X = -4/5 and X is in Quadrant 4, then find Cos 2X

    I have used the Double Angle ID and I got -7/25 as my answer.

    However, here is where my problem is at. The question says that X is in Q4, so therefore Cos has to be positive right?

    This was a question that I did on my Trig test and I got it wrong...the choices were...

    A. -24/25
    B. -7/25
    C. 24/25
    D. 7/25

    I chose D because Cos is positive in Q4, however the correct answer was B, the exact same answer I got when I used the double angle formula...but it says X is in Q4????

    Can somebody explain this to me please? Thanks!

    omg someone please answer me
    Last edited by iAlphaBeasti; April 26th 2009 at 10:57 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Quote Originally Posted by iAlphaBeasti View Post
    If Sin X = -4/5 and X is in Quadrant 4, then find Cos 2X

    I have used the Double Angle ID and I got -7/25 as my answer.

    However, here is where my problem is at. The question says that X is in Q4, so therefore Cos has to be positive right?

    This was a question that I did on my Trig test and I got it wrong...the choices were...

    A. -24/25
    B. -7/25
    C. 24/25
    D. 7/25

    I chose D because Cos is positive in Q4, however the correct answer was B, the exact same answer I got when I used the double angle formula...but it says X is in Q4????

    Can somebody explain this to me please? Thanks!
    cos 2x = 1 - 2sin^2 x
    = 1 - 2(-4/5)2
    = 1 - 32/25
    = -7/25

    cos x would be positive in Q4 but cos 2x is a different proposition

    If x is in Q4 then 2x is in Q3 or Q4
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    3
    Quote Originally Posted by Glaysher View Post
    cos 2x = 1 - 2sin^2 x
    = 1 - 2(-4/5)2
    = 1 - 32/25
    = -7/25

    cos x would be positive in Q4 but cos 2x is a different proposition

    If x is in Q4 then 2x is in Q3 or Q4
    what do you mean different proposition? could you elaborate it a little bit more?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Quote Originally Posted by iAlphaBeasti View Post
    what do you mean different proposition? could you elaborate it a little bit more?
    Cos (angle) is positive if the angle in is Q4

    You only know that x is in Q4 ie 270 - 360 degrees so cos x is positive

    But 2x would range between 540 (180) and 720 (360) degrees putting 2x in either Q3 or Q4 depending on what the original x actually was

    And Cos (angle) is negative if the angle is in Q3
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2009
    Posts
    3
    Quote Originally Posted by Glaysher View Post
    Cos (angle) is positive if the angle in is Q4

    You only know that x is in Q4 ie 270 - 360 degrees so cos x is positive

    But 2x would range between 540 (180) and 720 (360) degrees putting 2x in either Q3 or Q4 depending on what the original x actually was

    And Cos (angle) is negative if the angle is in Q3
    Yeah but it could also be positive if it was in Q4 like you say so how would I know which choice to choose? sorry for all the questions.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Glaysher's Avatar
    Joined
    Aug 2006
    From
    Newton-le-Willows
    Posts
    224
    Quote Originally Posted by iAlphaBeasti View Post
    Yeah but it could also be positive if it was in Q4 like you say so how would I know which choice to choose? sorry for all the questions.
    It could have been postive without doing the working out but when we applied the cos 2x formula we got a negative answer fixing 2x in Q3

    cos 2x = 1 - 2sin^2 x
    = 1 - 2(-4/5)^2
    = 1 - 32/25
    = -7/25

    However if the question had said sin x = -1/5 and x is in Q4 we would have got:

    cos 2x = 1 - 2sin^2 x
    = 1 - 2(-1/5)^2
    = 1 - 2/25
    = 23/25

    and so in this specific case 2x would have been in Q4
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. has my teacher been wrong here..
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: August 28th 2009, 02:43 AM
  2. Replies: 6
    Last Post: August 12th 2009, 03:15 AM
  3. Replies: 3
    Last Post: August 11th 2009, 05:54 PM
  4. my teacher marked this wrong on the test
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 10th 2008, 04:06 AM
  5. Double and triple integral issues
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 23rd 2008, 11:21 PM

Search Tags


/mathhelpforum @mathhelpforum