trig equation?

Question

How do you solve sin x + cos x = 0

Answer 1

Sin and cosine are equal and opposite a when x=135 degrees and when x=315 degrees.

Answer 2

i think of it as finding a point on the unit circle where the magnitudes of x and y are the same, but the signs are opposite. this narrows it down to the 2nd or 4th quadrants( where signs are opposite). the answer will also be a multiple of pi/4 since these points are where x and y have the same magnitude(or abs(x) = abs(y). the 2 solutions then are 3*pi/4 and 7*pi/4

Answer 3

sin x + cos x = 0
take square:
(sin x)^2 + (cos x)^2 +2 * sin x * cos x = 0
1 + 2 * sin 2x = 0
sin 2x = -1/2
2 x = 210 degrees
x = 105 degrees

I'm not sure, since it was 6 years ago, i studied this staff....

Answer 4

well for this sort of equation I would move the sinx to the other side.
cosx= - sinx, then ask yourself the question where will the cosx equal the negative sinx?

So if you think of the unit circle think of your 45 degrees, so your pie/4's.

Try going from there.

Answer 5

sinx+cosx=0 or
cosx=-sinx
we know that:
cos(a+b)=cosacosb-sinasinb
and cos(pi/2+x)=cos(pi/2)cosx-sin(pi/2)sinx
cos(pi/2+x)=0cosx-1sinx
cos(pi/2+x)=-sinx
then,
cosx=cos(pi/2+x)
homogeneous in cosine.
there are 2 solutions for x:
x=2kpi+or-(pi/2+x)
x=2kpi+pi/2+x (1) and x=2kpi-pi/2-x (2)
solve (2):
2x=2kpi-pi/2 or
x=kpi-pi/4
set: k=0 ; k=1 ; k=2 ; k=3 and so on.
for k=0 ; x=0pi-pi/4 or x=-pi/4
for k=1 ; x=1*pi-pi/4 or x=3pi/4
for k=2 ; x=2pi-pi/4 or x=7pi/4
for k=3 ; x=3pi-pi/4 or x=11pi/4
and so on.