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I need to convert the rectangular equation to polar form

x*y=1

so far I got

r^2×cos(x)×sin(x)=1

but I'm pretty sure it can be further simplified ?? help pls

Verified Answer :

AL2006

You don't want 'x' in the polar form.  The arguments
of the sin and cos should be angles.

You're doing great.  You're already through the tough part.
You knew that  x = r cos(α)  and  y = r sin(α)  .
The correct equation for where you stopped is

                              x· y  =  r² · cos(α) · sin(α)  =  1

You can simplify it a little if you remember the 'double-angle' equation:

                             sin(2α)  =  2 · sin(α) · cos(α)

So      cos(α) · sin(α)  =  (1/2) sin(2α)

and              r² · cos(α) · sin(α)  =  1

                   r² · sin(2α)  =  2 

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