EXPLORE The Cartesian coordinates of a point in the xy plane are (-4.7, -1.4). F

Question

EXPLORE The Cartesian coordinates of a point in the xy plane are (-4.7, -1.4). 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 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 Determine the distance r from the origin using the following equation: r = = m Determine the polar angle using the following equation: tan theta = y/x = -1.4 m/-4.7 m which gives theta = tan-1 Taking care to consider that there is more than one possible theta whose tangent function equals any given positive number, and choosing theta to have a value in the correct quadrant, gives theta= Note that you must use the signs of x and y to find that the point lies in the third quadrant of the coordinate system.

Explanation / Answer

here we have 1. r = sqrt( x^2 + y^2) => sqrt( 4.7^2 + 1.4^2) => 4.9m 2. @ = tan ^-1(0.30) => since both x and y are negative, thus we have @ to be in 3th quadrant so @ =180 + 16.69 => @= 196.69

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