Results 1 to 3 of 3

Math Help - sin(x) = -cos(x)

  1. #1
    Newbie
    Joined
    Dec 2006
    Posts
    6

    sin(x) = -cos(x)

    sin(x) = -cos(x), find x
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by stupid_kid View Post
    sin(x) = -cos(x), find x
    Suppose sin(x)>0 (sin and cos cannot both be simultaneously 0 so don't
    worry about that possibility). Then cos(x)<0, and x is in the second
    quadrant. In the first quadrant sin(x)=cos(x) means x=pi/4 (that is 45
    degrees), so here x =pi - pi/4 = 3 pi/4 (that is 135 degrees).

    Now suppose that sin(x)<0, then cos(x)>0 and we are in the fourth quadrant, and so x=-pi/4 (that is -45 degrees which is also +315 degrees).

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,911
    Thanks
    775
    Hello, kid!

    sin(x) = -cos(x). .Find x.
    . . . . . . . . . . . . . . . . . . . . . sin(x)
    Divide both sides by cos(x): . -------- .= .-1
    . . . . . . . . . . . . . . . . . . . . . cos(x)

    And we have: .tan(x) .= .-1


    Therefore: .x .= .π + πk, for any integer k.

    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum