Plot the point on the polar coordinate system. ( − 2 , 2 π 3 ) (-2,\frac{2\pi}{3}) ( − 2 , 3 2 π )

Here we're asked to plot the point on the polar coordinate system, and the point that we're given is a negative 2, 2 pi over 3. So I have an r value of negative 2 and a theta value of 2 pi over 3. So first, locating my angle at 2 pi over 3 radians, I'm going to end up right along this line. But because I have an r value that is a negative, that tells me that I need to count in the opposite direction rather than in this direction that I would if I had a positive r value. So here, I'm going to count 1, 2 in that opposite direction of my angle, and this is where my point will be. 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.
$(-2,\frac{2\pi}{3})$

Polar coordinate system showing point (-2, 2π/3) marked 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 from the positive x-axis.

The given polar coordinate is (-2, \frac{2\pi}{3}). The negative radius indicates that the point is in the opposite direction of the angle.

First, locate the angle \frac{2\pi}{3} on the polar coordinate system. This angle is in the second quadrant, 120 degrees from the positive x-axis.

Since the radius is negative, move 2 units in the opposite direction of the angle \frac{2\pi}{3}. This means you will move 2 units in the direction of the angle \frac{5\pi}{3} (or 300 degrees), which is directly opposite to \frac{2\pi}{3}.

Plot the point at this location, which should be in the fourth quadrant, 2 units from the origin along the line of \frac{5\pi}{3}.