Question

Sin(x)=-Cos(x)

Answer 1

what about it
find all x?

Answer 2

Graph or algebra? i like to use a picture of the unit circle

Answer 3

What are the values of x

Answer 4

Picturing it in your head you can figure it out, but I'm sure others have a more formal way.

Answer 5

As I said before, this equation suggests that x is a point at which sin and cos are equal but with different signs. That means it's the picture of \(\frac{\pi}{4}\) on the second and fourth quadrants.

Answer 6

From here we can say assuming \(x\in [0,2\pi)\), that the solutions are \(x=\pi-\frac{\pi}{4}=\frac{3\pi}{4}\) or \(x=2\pi-\frac{\pi}{4}=\frac{7\pi}{4}\).

Answer 7

The solution over all real numbers is then \(x=\frac{3\pi}{4}+n\pi\), where \(n=0,\pm 1, \pm 2,\dots\).

Answer 8

\[\large ThankYou:)\]

Answer 9

Hm 1 more thing

Answer 10

there is another way of doing this as well

Answer 11

if you square both sides you get:\[\sin^2(x)=\cos^2(x)=1-\sin^2(x)\]\[2\sin^2(x)=1\]\[sin(x)=\pm\frac{1}{\sqrt{2}}\]

Answer 12

Sin(x)=-Cos(x)
-tan(x) = 1
-tan^2(x) = 1^(2)
1+tan^2(x) = sec^2(x)
sec^2(x)
cant you simplify it to
sec^2(x)

Answer 13

but @asnaseer you will have extra solutions with that
we will have
sin(x)=cos(x) solutions as well

Answer 14

actually @cuddlepony you have found an even simpler method:\[\tan(x)=-1\]solve for x.

Answer 15

oh yeah lol :P

Answer 16

Ok Thanks Mr.Math, asnaseer ,Cuddlepony &Turing Test
I got it :)

Answer 17

yes @TuringTest - my way includes solutions that are not valid for the original problem - well spotted :-)

Answer 18

You're welcome Diya! :)

Answer 19

I have another question !