Convert the point to polar coordinates.(0,5)(0,5)(0,5)

( 5 , π 2 ) (5,\frac{\pi}{2}) ( 5 , 2 π )

Convert the point to polar coordinates. ( 0 , 5 ) (0,5) ( 0 , 5 )

Here we're asked to convert the point given in rectangular coordinates into polar coordinates, and the point that we're given here is zero five. So let's get started with our steps and go ahead and plot our point. Now plotting our point at zero five ends me up right here on this on the top of my y axis, and now I can move on to step two and calculate my r value. Now in finding my r value, I get that r is going to be equal to the square root of zero squared plus five squared, which is really just going to be equal to the square root of 25 or just five. Now something that you may have noticed here is that whenever you have one of your x or y values being zero, your r value is actually just always going to be equal to whatever your other number was. So here, it's five just as it should be, but you can always fall back on that equation. If you forget that or just skip over it, you can still get to your r value the same way. Now with step two done, let's move on to step three and calculate beta. Now here, looking at the location of my point, I see that it is on an axis, and it's specifically on that positive y axis, which is exactly where my angle pi over two is located in polar coordinates. So that tells me that my theta value here is simply pi over two. No calculations needed. Now we have our point in polar coordinates located at five pi over two, and we are completely done here. Thanks for watching, and let me know if you have questions.

Convert the point to polar coordinates. ( 0 , 5 ) (0,5) ( 0 , 5 )

( 5 , π 2 ) (5,\frac{\pi}{2}) ( 5 , 2 π )

( − 5 , π 2 ) (-5,\frac{\pi}{2}) ( − 5 , 2 π )

16. Parametric Equations & Polar Coordinates

Polar Coordinates

Calculus

16. Parametric Equations & Polar Coordinates

Polar Coordinates

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Multiple Choice

Convert the point to polar coordinates.
$(0,5)$

$(0,0)$

$(5,0)$

$(-5,\frac{\pi}{2})$

$(5,\frac{\pi}{2})$

Verified step by step guidance

Step 1: Recall the formula for converting Cartesian coordinates (x, y) to polar coordinates (r, θ). The radius r is calculated as r = √(x² + y²), and the angle θ is calculated as θ = arctan(y/x).

Step 2: Identify the given Cartesian coordinates. In this case, the point is (0, 5), where x = 0 and y = 5.

Step 3: Calculate the radius r. Substitute x = 0 and y = 5 into the formula r = √(x² + y²). This simplifies to r = √(0² + 5²) = √(25).

Step 4: Determine the angle θ. Since x = 0, the point lies directly on the positive y-axis. The angle θ is π/2 radians (90 degrees) because the positive y-axis corresponds to this angle in polar coordinates.

Step 5: Combine the radius r and angle θ to express the polar coordinates. The polar coordinates are (r, θ), which simplifies to (5, π/2).

5:32m

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