# equivalence relation trig. function

• May 7th 2008, 11:45 AM
riptorn70
equivalence relation trig. function

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.
• May 7th 2008, 11:58 AM
flyingsquirrel
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 $\sin^2y+\cos^2z=1$)
• May 7th 2008, 12:03 PM
riptorn70
Thankyou flying squirrel that really helped.
Riptorn70