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 six, negative 11 pi over six. So here I have an r value of six and a theta value of negative 11 pi over six. 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 six radians, I end up right along this line. Now counting out using that r value of six, counting out to six on that line lands me right here. So this is my point, six negative 11 pi over six. Let me know if you have any questions.

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.
$(6,-\frac{11\pi}{6})$

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

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: Analyze the given polar coordinate (6, -11π/6). Here, 'r = 6' indicates the point is 6 units away from the origin, and 'θ = -11π/6' is the angle in radians. Negative angles are measured clockwise from the positive x-axis.

Step 3: Convert the negative angle to a positive equivalent if needed. Since angles in polar coordinates are periodic, adding 2π to -11π/6 gives the equivalent positive angle: θ = -11π/6 + 2π = π/6.

Step 4: Locate the angle π/6 on the polar coordinate system. This angle lies in the first quadrant, 30 degrees counterclockwise from the positive x-axis.

Step 5: Plot the point. From the origin, move along the direction of the angle π/6 and mark the point at a radial distance of 6 units. This is the correct location of the point (6, -11π/6) on the polar coordinate system.