Plot the point on the polar coordinate system. ( 6 , − 11 π 6 ) (6,-\frac{11\pi}{6}) ( 6 , − 6 11 π )

Here we're asked to plot the point on the polar coordinate system, and the point that we're given is 6, negative 11 pi over 6. So here I have an r value of 6 and a theta value of negative 11 pi over 6. Now we wanna locate our angle theta first, of course, and because this is a negative angle, that tells me that I want to measure it clockwise rather than counterclockwise. So going around clockwise, negative 11 pi over 6 radians, I end up right along this line. Now counting out using that r value of 6, counting out to 6 on that line lands me right here. So this is my point, 6 negative 11 pi over 6. Let me know if you have any 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.
$(6,-\frac{11\pi}{6})$

Polar coordinate system showing point (6, -11π/6) marked in red.

Verified step by step guidance

Identify the polar coordinates given: (6, -\frac{11\pi}{6}). The first value, 6, is the radius (r), and the second value, -\frac{11\pi}{6}, is the angle (\theta) in radians.

Convert the negative angle to a positive angle by adding 2\pi. Since -\frac{11\pi}{6} is negative, add 2\pi to find the equivalent positive angle: -\frac{11\pi}{6} + 2\pi = \frac{\pi}{6}.

Locate the angle \frac{\pi}{6} on the polar coordinate system. This angle is in the first quadrant, 30 degrees from the positive x-axis.

From the origin, move along the direction of the angle \frac{\pi}{6} to a distance of 6 units, as indicated by the radius.

Plot the point at the intersection of the line at angle \frac{\pi}{6} and the circle with radius 6. This is the correct location of the point (6, -\frac{11\pi}{6}) on the polar coordinate system.