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

1. ## sin(x) = -cos(x)

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

2. Originally Posted by stupid_kid
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
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

3. 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 .= .¾π + πk, for any integer k.