Find an equivalent equation in rectangular coordinates.
-$\mathrm { r } ( \cos \theta - \sin \theta ) = 5$
A) $x - y = 5$
B) $\sqrt { x ^ { 2 } + y ^ { 2 } } ( x - y ) = 5$
C) $x + y = 5$
D) $x - y = 25$

Question

Quizplus · Accepted Answer

In polar coordinates, $r = \sqrt{x^2 + y^2}$, $\cos\theta = \frac{x}{r}$, and $\sin\theta = \frac{y}{r}$. Substituting these into the given equation, we get $r(\frac{x}{r} - \frac{y}{r}) = 5$, which simplifies to $x - y = 5$.

Find an Equivalent Equation in Rectangular Coordinates r(cos⁡θ−sin⁡θ)=5\mathrm { r } ( \cos \theta - \sin \theta ) = 5r(cosθ−sinθ)=5

Find an Equivalent Equation in Rectangular Coordinates $\mathrm { r } ( \cos \theta - \sin \theta ) = 5$