Question

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

Answer 1

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