Convert the polar equation r=(5)/(2sin theta-3cos theta) to rectangular form.

Remember Trig Identities: We have: r = 5 / (2sin θ - 3cos θ). First, let's remember that sin θ = y/r and cos θ = x/r.Substitute Trig Identities: Substitute sin θ and cos θ in the equation: r = 5 / (2(y/r) - 3(x/r)).Simplify Equation: Simplify the equation: r = 5r / (2y - 3x).Eliminate Fraction: Multiply both sides by (2y - 3x) to get rid of the fraction: r(2y - 3x) = 5r.Use Polar Coordinates: Remember that r^2 = x^2 + y^2. But we need to use r correctly in our equation.

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Convert the polar equation $\newline$ $r=\frac{5}{2\sin \theta-3\cos \theta}$ to rectangular form.

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Q. Convert the polar equation

\newline

r=\frac{5}{2\sin \theta-3\cos \theta}

to rectangular form.

Remember Trig Identities: We have: $r = \frac{5}{2\sin \theta - 3\cos \theta}$ . First, let's remember that $\sin \theta = \frac{y}{r}$ and $\cos \theta = \frac{x}{r}$ .
Substitute Trig Identities: Substitute $\sin \theta$ and $\cos \theta$ in the equation: $r = \frac{5}{2(\frac{y}{r}) - 3(\frac{x}{r})}.$
Simplify Equation: Simplify the equation: $r = \frac{5r}{2y - 3x}$ .
Eliminate Fraction: Multiply both sides by $(2y - 3x)$ to get rid of the fraction: $r(2y - 3x) = 5r$ .
Use Polar Coordinates: Remember that $r^2 = x^2 + y^2$ . But we need to use $r$ correctly in our equation.