QuestionFind the polar coordinates, and , of the point given in Cartesian coordinates. A) B) C) D)
Studdy Solution
STEP 1
1. The given point in Cartesian coordinates is .
2. We need to convert these Cartesian coordinates to polar coordinates .
3. The polar coordinates must satisfy and .
STEP 2
1. Calculate the radius .
2. Determine the angle .
3. Match the calculated polar coordinates with the given options.
STEP 3
Calculate the radius using the formula for the distance from the origin in the Cartesian plane:
For the point :
STEP 4
Calculate the angle using the arctangent function, considering the signs of and :
For the point :
The angle where and considering the point is in the fourth quadrant (since and ), is:
STEP 5
Match the calculated polar coordinates with the given options:
A)
B)
C)
D)
The correct match is option B: .
The polar coordinates of the point are:
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