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 three y minus five x is equal to two. 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 our sine theta for our X and Y values here. This gives me that three r sine theta minus five r cosine theta is equal to two. 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 three sine theta minus five cosine theta is all equal to two on that right side. Now from here, all that's left to do is divide. So I divide both sides by a three sine theta minus five 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 two over three sine theta minus five 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

16. Parametric Equations & Polar Coordinates

Polar Coordinates

Calculus

16. Parametric Equations & Polar Coordinates

Polar Coordinates

Struggling with Calculus?

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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

Step 1: Recall the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). In polar coordinates, x = r * cos(θ) and y = r * sin(θ). Substitute these expressions into the given Cartesian equation.

Step 2: Replace x with r * cos(θ) and y with r * sin(θ) in the equation 3y - 5x = 2. This gives 3(r * sin(θ)) - 5(r * cos(θ)) = 2.

Step 3: Factor out r from the terms involving sin(θ) and cos(θ). The equation becomes r * (3 * sin(θ) - 5 * cos(θ)) = 2.

Step 4: Solve for r by dividing both sides of the equation by (3 * sin(θ) - 5 * cos(θ)). This results in r = 2 / (3 * sin(θ) - 5 * cos(θ)).

Step 5: The polar form of the equation is now expressed as r = 2 / (3 * sin(θ) - 5 * cos(θ)). Ensure the denominator is not zero to avoid undefined values.

5:32m

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