When is cos(x) - sin(x) < cos(x) + sin(x) for 0 ≤ x ≤ 2π?

[rad0786]

Homework Statement

for what values of x is cos(x) - sin(x) < cox(x) + sin(x) where 0 =< x =< 2pi

Homework Equations

none.

The Attempt at a Solution

I actually drew out the funtions and added them.
In my graphs, I get that:

cos(x) - sin(x) < cos(x) + sin(x) for for 0 =< x =< pi

When I try to show this in Matlab, i ger messy results?

Any ideas?

 

[neutrino]

There's a simpler way to do it. Did you try algebraically manipulating the equation?

 

[rad0786]

no ... infact, I am not sure what you mean?

cos(x) - sin(x) < cos(x) + sin(x)
cos(x) - cos(x) < sin(x) + sin(x)
0 < 2sin(x)
0 < sin(x)

and sin(x) is bigger than zero for 0 =< x =<pi/2

This dosn't seem right to me...

 

[neutrino]

Actually, sin(x)>0 everywhere on the open interval (0,pi).

 

[rad0786]

oh yeah, sorry, i got confused...

so that means that cos(x) - sin(x) is less than cos(x) + sin(x) for (0,pi) ?

 

[neutrino]

Yes. 10char[/color]

 

[rad0786]

i don't like this because it dosn't match up with my graphs.

but the math looks right, therefore, their must exist an error in my graphs.

 

[rad0786]

opps, it actually does match with my graphs... :)