equivalence relation trig. function

**riptorn70** · May 7th 2008, 11:45 AM

Please can somebody help.

The $\sim$ relation on $\Re$ is defined by x $\sim$ y if and only if $\sin ^2 x + \cos^2 y = 1$ .
Show that $\sim$ is an equivalence relation on $\Re$ .

Your help would be much appreciated.
riptorn70.

**flyingsquirrel** · May 7th 2008, 11:58 AM

Hi

You need to show three things :

$x\sim x$
$x\sim y \Leftrightarrow y\sim x$ (hint : use $\sin^2t+\cos^2t=1$ )
$(x \sim y \text{ and } y\sim z) \Rightarrow x\sim z$ (hint : sum the two relations $\sin^2x+\cos^2y=1$ and $\sin^2y+\cos^2z=1$ )