Plot the point on the polar coordinate system. ( 5 , 210 ° ) (5,210°) ( 5 , 210° )

Hey, everyone. In this problem, we're asked to plot the point on the polar coordinate system. And the point that we're given is 5210 degrees. So here I have an r value of 5 and a theta value of 210 degrees. Now remember when plotting in polar coordinates we want to locate that angle first, In this case, 210 degrees. Now if you're given a polar coordinate system in radians, you can feel free to go ahead and convert this value if needed. Or if you already know where 210 degrees is located based on these radian angle measures, you can go ahead and go there. Now since I know these values, if I go to 210 degrees, that's the same thing as 7 pi over 6. So I know that my point will be along this line. Now using that r value to count out to 1, 2, 3, 4, 5, my point ends up being right here and we have plotted this point in polar coordinates. 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.
$(5,210°)$

Polar coordinate system showing point (5, 210°) marked in red.

Verified step by step guidance

Identify the polar coordinates given: (5, 210°). This means the point is 5 units away from the origin at an angle of 210° from the positive x-axis.

Convert the angle from degrees to radians if necessary. Since 210° is a common angle, it can be converted to radians as 210° = $ \frac{7\pi}{6} $ radians.

Locate the angle $ \frac{7\pi}{6} $ on the polar coordinate system. This angle is in the third quadrant, as it is more than $ \pi $ (180°) but less than $ \frac{3\pi}{2} $ (270°).

From the origin, measure a distance of 5 units along the direction of the angle $ \frac{7\pi}{6} $.

Plot the point at this location. The correct plot should be in the third quadrant, 5 units from the origin, along the line corresponding to $ \frac{7\pi}{6} $.