Plot the point on the polar coordinate system. ( − 3 , − 90 ° ) (-3,-90°) ( − 3 , − 90° )

Here we're asked to plot the point on the polar coordinate system, and the point that we're given is negative three, negative 90 degrees. So here I have an r value of negative three and a theta value of negative 90 degrees. Now remember when dealing with a negative angle, that means that we're measuring our angle clockwise rather than counterclockwise. So locating our angle first here, I know that I need to go clockwise 90 degrees, which will end me up on this line here, one of my quadrantal angles. Now I need to go ahead and use that r value. But here, my r value is actually also negative. So here, that tells me that I'm not going to count out this way as I would for a positive r value, but rather in the opposite direction, in this case, up. So I'm going to count one, two, three, and I'm going to end up right here for this final point. Thanks for watching, and let me know if you have questions.

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16. Parametric Equations & Polar Coordinates7h 58m

16. Parametric Equations & Polar Coordinates

Polar Coordinates

Calculus

16. Parametric Equations & Polar Coordinates

Polar Coordinates

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Multiple Choice

Plot the point on the polar coordinate system.
$(-3,-90°)$

Polar coordinate system showing point (-3, -90°) plotted in red.

Polar coordinate system showing point (2, 0°) plotted in red.

Polar coordinate system showing point (3, 90°) plotted in red.

Polar coordinate system showing point (3, -90°) plotted in red.

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Verified step by step guidance

Step 1: Understand the polar coordinate system. In polar coordinates, a point is represented as (r, θ), where 'r' is the radial distance from the origin and 'θ' is the angle measured counterclockwise from the positive x-axis.

Step 2: Analyze the given point (-3, -90°). The negative radial distance (-3) indicates that the point is located in the opposite direction of the angle -90°. The angle -90° corresponds to the negative y-axis in standard polar coordinates.

Step 3: Adjust the negative radial distance. To plot the point, convert the negative radial distance to a positive one by adding 180° to the angle. This transforms the point (-3, -90°) to (3, 90°).

Step 4: Locate the angle 90° on the polar coordinate system. The angle 90° corresponds to the positive y-axis. Identify the radial distance of 3 units along this direction.

Step 5: Plot the point (3, 90°). Starting from the origin, move 3 units along the positive y-axis to mark the point on the polar coordinate system.