QuestionSketch the polar coordinates .
Studdy Solution
STEP 1
Assumptions1. The given polar coordinates are
. The first value in the polar coordinate pair, , represents the radius (r) and the second value, , represents the angle (θ) in radians.
3. The radius can be negative, which means the point is in the opposite direction of the angle.
4. The angle is measured counter-clockwise from the positive x-axis.
STEP 2
First, we need to normalize the angle. This is because the angle is more than , which is a full revolution in radians. We can do this by subtracting from the angle until it falls within the range to .
STEP 3
Now, plug in the given values for and calculate the new angle.
STEP 4
Next, we need to consider the negative radius. A negative radius means that the point is in the opposite direction of the angle. We can handle this by adding to the angle and making the radius positive.
STEP 5
Calculate the new angle.
STEP 6
Now that we have the normalized polar coordinates , we can sketch the point on a polar coordinate plane.1. Start at the origin (0,0).
2. Rotate radians counter-clockwise from the positive x-axis.
3. Move6 units out from the origin in the direction of the angle.
The point in polar coordinates corresponds to the point after normalization, which can be sketched on the polar coordinate plane.
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