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

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- Apr 8th 2007, 03:06 AMstupid_kidsin(x) = -cos(x)
sin(x) = -cos(x), find x

- Apr 8th 2007, 04:24 AMCaptainBlack
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 - Apr 8th 2007, 04:58 AMSoroban
Hello, kid!

Quote:

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.*