sin(x) = -cos(x), find x

Results 1 to 3 of 3

- April 8th 2007, 02:06 AM #1

- Joined
- Dec 2006
- Posts
- 6

- April 8th 2007, 03:24 AM #2

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 4

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

- April 8th 2007, 03:58 AM #3

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,809
- Thanks
- 701

Hello, kid!

sin(x) = -cos(x). .Find x.

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

. . . . . . . . . . . . . . . . . . . . . cos(x)

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

Therefore: .x .= .¾π + πk, for any integer*k.*