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

9. Polar Equations

Convert Equations Between Polar and Rectangular Forms

Trigonometry

9. Polar Equations

Convert Equations Between Polar and Rectangular Forms

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

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

To solve for r, divide both sides of the equation by (3sin(θ) - 5cos(θ)): r = 2 / (3sin(θ) - 5cos(θ)).

This is the polar form of the given equation, which matches one of the provided options.

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