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 five, two hundred and ten degrees. So here I have an r value of five and a theta value of two hundred and ten degrees. Now remember when plotting in polar coordinates, we want to locate that angle first, in this case two ten 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 two ten degrees that's the same thing as seven pi over six, so I know that what my point will be along this line. Now using that r value to count out to one, two, three, four, five my point ends up being right here and we have plotted this point in polar coordinates. Let me know if you have any questions.

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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.
$(5,210°)$

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

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Verified step by step guidance

Step 1: Understand the polar coordinate system. A polar coordinate 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: Identify the given polar coordinates. In this case, the point is (5, 210°), where 'r' = 5 and 'θ' = 210°.

Step 3: Convert the angle θ from degrees to radians if necessary. Recall that 210° can be converted to radians using the formula θ (radians) = θ (degrees) × π/180. This gives θ = 210 × π/180 = 7π/6 radians.

Step 4: Locate the angle θ = 7π/6 on the polar coordinate system. This angle lies in the third quadrant, as it is greater than π but less than 3π/2.

Step 5: From the origin, move outward along the line corresponding to θ = 7π/6 until you reach the radial distance of r = 5. Mark the point at this location on the polar coordinate system.