Question

solve for x
Cos x - sin x = 1

Answer 1

well what is 1-0?

Answer 2

or in other words when is cos(x)=1 and sin(x)=0

Answer 3

at 0pi

Answer 4

I know that would give one kinda solution
we could also find a solution be considering 0-(-1)

Answer 5

so 0+2pi*n
where n is integer for when cos(x)=1 and sin(x)=0

Answer 6

what answer would get considering 0-(-1) now

Answer 7

1

Answer 8

how about x=45?

Answer 9

that isn't what i meant but yeah 0-(-1) is 1

Answer 10

no nvm

Answer 11

so we have cos(x)-sin(x)=1
and we know on the unit circle somewhere we will have
0 -(-1)=1
so when is cos(x)=0 and sin(x)=-1

Answer 12

I thought =0, for some reason... don't know why. srry abt that

Answer 13

sin is 0 at x= pi/2 and 3pi/2. cos is 0 at x= 0pi and pi

Answer 14

sin is 1 at x=pi/2 and sin is -1 at x=3pi/2
sin is 0 at x=0,x=pi
cos is 0 at x=pi/2 and 3pi/2
cos is 1 at x=0
cos is -1 at x=pi
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cos(x)-sin(x)=1
1-0=1 so cos(x)=1 when x=0,2pi
n is integer
cos(x)-sin(x)=1
0-(-1)=1 so sin(x)=-1 when x=3pi/2
if we are solving in the 0 to 2pi interval


I don't see that pi is a solution though
cos(pi)=-1

Answer 15

you can skip the line where n is integer
I was thinking about giving the general solution
but I will let you come up with that

Answer 16

thanks guys!! :D