x^2-y^2=5
I see examples of people adding r, but I'm not understanding how. this is my first experience with trig taking in precalc.
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The way to convert rectilinear coordinates (x, y) to polar coordinates is $\displaystyle ( r, \theta)$ is
$\displaystyle x = r~cos(\theta)$
$\displaystyle y = r~sin(\theta)$
So what is $\displaystyle x^2 - y^2 = (r~cos( \theta))^2 - (r~sin(\theta))^2$
Can you take it from here?
-Dan
You have $\displaystyle r^2cos^2(\theta)- r^2sin^2(\theta)= 5$. You can factor out $\displaystyle r^2$ from both sides to get $\displaystyle r^2(cos^2(\theta)- sin^2(\theta))= 5$. If you do not consider that sufficient as an answer, you can use the trig identity $\displaystyle cos^2(\theta)- sin^2(\theta)= cos(2\theta)$ to write $\displaystyle r^2 cos(2\theta)= 5$.