Question

inequality help!
medal & fan!

Answer 1

\[\sqrt2\sin x+\sqrt2\cos x>0\quad\Longleftrightarrow\quad\sin x+\cos x>0\]
Also at what x do \(\sin x = -\cos x\) (or \(\sin x+\cos x=0\))?

Answer 2

x would equal -45, correct?

Answer 3

Yeah, but we are focusing on \(0<x<2\pi\)

But you can just add \(360^\text o\) and get \(315^\text o\) (or \(\dfrac{7\pi}{4}\)).

But it's isn't only x value. Maybe try sketch sine and cosine

Answer 4

so \[\frac{ 7\pi }{ 4 }<x <2\pi\]