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 5. So let's get started with our steps and go ahead and plot our point. Now plotting our point at 5 ends me up right here on this on the top of my y axis. And now I can move on to step 2 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 0 squared plus 5 squared, which is really just going to be equal to the square root of 25 or just 5. Now something that you may have noticed here is that whenever you have one of your x or y values being 0, your r value is actually just always going to be equal to whatever your other number was. So here, it's 5 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 2 done, let's move on to step 3 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 2 is located in polar coordinates. So that tells me that my theta value here is simply pi over 2. No calculations needed. Now we have our point in polar coordinates located at 5pi over 2, 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 )

9. Polar Equations

Convert Points Between Polar and Rectangular Coordinates

Trigonometry

9. Polar Equations

Convert Points Between Polar and Rectangular 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

Understand that polar coordinates are represented as (r, θ), where r is the radius or distance from the origin, and θ is the angle from the positive x-axis.

Identify the given Cartesian coordinates: (0, 5). This means the point is located on the y-axis, 5 units above the origin.

Calculate the radius r using the formula r = \sqrt{x^2 + y^2}. For the point (0, 5), this becomes r = \sqrt{0^2 + 5^2} = \sqrt{25} = 5.

Determine the angle θ. Since the point is on the positive y-axis, the angle θ is \frac{ ext{π}}{2} radians, which corresponds to 90 degrees.

Combine the radius and angle to express the point in polar coordinates: (5, \frac{ ext{π}}{2}).

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