QuestionSketch the polar point (-6, -25π/12).
Studdy Solution
STEP 1
Assumptions1. The polar coordinates are given as . The first value in the pair represents the radial coordinate (r), which is the distance from the origin to the point3. The second value in the pair represents the angular coordinate (θ), which is the angle formed by the positive x-axis and the line segment from the origin to the point4. The angle is measured in radians5. The angle is negative, which means it is measured clockwise from the positive x-axis6. The radial coordinate is negative, which means the point is in the opposite direction of the angle θ from the origin
STEP 2
First, we need to convert the negative angle to a positive angle. We can do this by adding to the negative angle until we get a positive angle.
where n is the smallest integer such that is positive.
STEP 3
Now, plug in the given value for the angle and calculate the positive angle.
STEP 4
Next, we need to deal with the negative radial coordinate. A negative radial coordinate means the point is in the opposite direction of the angle θ from the origin. So, we can convert the negative radial coordinate to a positive radial coordinate by adding to the angle.
STEP 5
Now, we need to convert the angle to an angle between0 and . We can do this by subtracting from the angle until we get an angle between0 and .
STEP 6
Now, we have the polar coordinates . We can plot this point on the polar coordinate system. The point is located6 units from the origin and forms an angle of with the positive x-axis, measured counterclockwise.
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