Explore The Cartesian coordinates of a point in the xy plane are ( -0.5, -4.5).

Question

Explore
The Cartesian coordinates of a point in the xy plane are ( -0.5, -4.5). Find the polar coordinates of the point.

Conceptualize
Note the Cartesian coordinates, the quadrant that the point of interest lies in, and the way the angle is defined for a point in that quadrant. Categorize

Categorize
We are given all the expressions to be used, and the problem is one of converting between polar and Cartesian coordinates in two dimensions.

Analyze
From the following equation:

and from the equation below:

which gives

Taking care to consider that there is more than one possible ? whose tangent function equals any given positive number, and choosing theta to have a value in the correct quadrant, gives

Explanation / Answer

tan(@)=4.5/0.5=9 therefore @= 92.95 degres (r=4.52773,@=92.95 degrees) is the polar form

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