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 3, negative 90 degrees. So here I have an r value of negative 3 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 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, for a positive r value, but rather in the opposite direction, in this case, up. So I'm going to count 1, 2, 3, and I'm going to end up right here for this final point. Thanks for watching, and let me know if you have questions.

9. Polar Equations

Polar Coordinate System

Trigonometry

9. Polar Equations

Polar Coordinate System

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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.

Verified step by step guidance

Understand that polar coordinates are given in the form (r, θ), where r is the radius (distance from the origin) and θ is the angle measured from the positive x-axis.

The given point is (-3, -90°). The negative radius means we will plot the point in the opposite direction of the angle.

Convert the angle from degrees to radians if necessary. Here, -90° is equivalent to -π/2 radians.

Since the radius is negative, plot the point 3 units away from the origin in the direction opposite to -90° (or -π/2 radians). This means moving 3 units in the direction of 90° (or π/2 radians).

Locate the point on the polar grid: move 3 units from the origin along the positive y-axis (since 90° corresponds to the positive y-axis).