Convert each equation to its polar form.3y−5x=23y-5x=23y−5x=2

r = 2 3 sin ⁡ θ − 5 cos ⁡ θ r=\frac{2}{3\sin\theta-5\cos\theta} r = 3 s i n θ − 5 c o s θ 2

Convert each equation to its polar form. 3 y − 5 x = 2 3y-5x=2 3 y − 5 x = 2

Here we're asked to convert the equation into its polar form, and the equation that we're given is 3 y minus 5 x is equal to 2. Remember that we can convert equations from their rectangular form into their polar form just using these equations here. So let's go ahead and sub in our cosine theta and r sine theta for our x and y values here. This gives me that 3 r sine theta minus 5 r cosine theta is equal to 2. Now since I have a r in both of these terms and my goal here is to solve for r, I'm gonna go ahead and factor that r out. This gives me r times 3 sine theta minus 5 cosine theta is all equal to 2 on that right side. Now from here, all that's left to do is divide. So I divide both sides by a 3 sine theta minus 5 cosine theta on both sides, having that subtraction there, then it will cancel out on that left side just leaving me with r as I intended. And then this will be equal to 2 over 3 sine theta minus 5 cosine theta, and this is my final answer since I have successfully solved for r here. I have no x's and y's left just r's and thetas. So this is my equation in its polar form. Thanks for watching and let me know if you have questions.

Convert each equation to its polar form. 3 y − 5 x = 2 3y-5x=2 3 y − 5 x = 2

r = 2 3 sin ⁡ θ − 5 cos ⁡ θ r=\frac{2}{3\sin\theta-5\cos\theta} r = 3 s i n θ − 5 c o s θ 2

r = 2 sin ⁡ θ − cos ⁡ θ r=\frac{2}{\sin\theta-\cos\theta} r = s i n θ − c o s θ 2

r = 3 sin ⁡ θ − 5 cos ⁡ θ r=3\sin\theta-5\cos\theta r = 3 sin θ − 5 cos θ

r = 3 5 sin ⁡ θ r=\frac35\sin\theta r = 5 3 sin θ

15. Polar Equations

Convert Equations Between Polar and Rectangular Forms

Precalculus

15. Polar Equations

Convert Equations Between Polar and Rectangular Forms

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Convert each equation to its polar form.
$3y-5x=2$

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

$r=\frac{2}{\sin\theta-\cos\theta}$

$r=3\sin\theta-5\cos\theta$

$r=\frac35\sin\theta$

Verified step by step guidance

Start by recalling the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). The equations are: x = r * cos(θ) and y = r * sin(θ).

Substitute x = r * cos(θ) and y = r * sin(θ) into the given Cartesian equation 3y - 5x = 2.

This substitution gives us: 3(r * sin(θ)) - 5(r * cos(θ)) = 2.

Factor out r from the left side of the equation: r(3 * sin(θ) - 5 * cos(θ)) = 2.

Solve for r by dividing both sides of the equation by (3 * sin(θ) - 5 * cos(θ)): r = 2 / (3 * sin(θ) - 5 * cos(θ)).

3:37m

Watch next

Master Convert Equations from Rectangular to Polar with a bite sized video explanation from Patrick

Start learning

Convert Equations Between Polar and Rectangular Forms practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice