Convert each equation to its polar form.x2+y2=2yx^2+y^2=2yx2+y2=2y

r = 2 sin ⁡ θ r=2\sin\theta r = 2 sin θ

Convert each equation to its polar form. x 2 + y 2 = 2 y x^2+y^2=2y x 2 + y 2 = 2 y

Here we're asked to convert the equation into its polar form and the equation that we're given is x squared plus y squared is equal to two y. So let's go ahead and dive in here by replacing x y and x squared plus y squared using these formulas. Now remember that if you have an x squared plus a y squared, you can simply replace this with r squared instead of using r cosine theta and r sine theta. So on that left side, all I have is r squared, and then this will be equal to two times r sine theta replacing that y value. Now from here I want to solve for r. So let's look at what's happening here. On both sides I have an r value. On that left side I have r squared and on that right side just an r. So that r on the right will cancel out with one of the r squareds on the left. Now that just leaves me with r on that left side and this is equal to two times the sine of theta and this gives me my final answer. This is my equation in its polar form. Let me know if you have any questions. Thanks for watching.

Convert each equation to its polar form. x 2 + y 2 = 2 y x^2+y^2=2y x 2 + y 2 = 2 y

r = 2 sin ⁡ θ r=2\sin\theta r = 2 sin θ

r = 2 r=\sqrt{2} r = 2 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z">

r = 4 sin ⁡ θ r=4\sin\theta r = 4 sin θ

r = 2 cos ⁡ θ r=2\cos\theta r = 2 cos 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.
$x^2+y^2=2y$

$r=\sqrt{2}$

$r=2\sin\theta$

$r=4\sin\theta$

$r=2\cos\theta$

Verified step by step guidance

Step 1: Recall the relationship between Cartesian coordinates (x, y) and polar coordinates (r, θ). The formulas are: x = r * cos(θ) and y = r * sin(θ). Additionally, x² + y² = r².

Step 2: Start with the given equation x² + y² = 2y. Substitute x² + y² with r², as x² + y² = r² in polar coordinates. This gives r² = 2y.

Step 3: Replace y with its polar form, y = r * sin(θ). Substituting this into the equation gives r² = 2 * r * sin(θ).

Step 4: Simplify the equation by dividing both sides by r (assuming r ≠ 0). This results in r = 2 * sin(θ).

Step 5: The polar form of the equation is now expressed as r = 2 * sin(θ). This is the final polar representation of the given Cartesian equation.

5:32m

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