Multiple Choice In a rectangular coordinate system, where...

Multiple Choice
In a rectangular coordinate system, where does the point with polar coordinates $\left(1,-\frac{\pi}{2}\right)$ lie?
(a) in quadrant IV
(b) on the $y$ -axis
(c) in quadrant II
(d) on the $x$ -axis

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Key Concepts

Polar Coordinate System

The polar coordinate system locates points in a plane using a distance from a fixed point (the pole) and an angle from a fixed direction (usually the positive x-axis). This system offers an alternative to the rectangular coordinate system, where points are described by x and y coordinates.

Conversion between Polar and Rectangular Coordinates

To translate polar coordinates (r, ?) into rectangular coordinates, the formulas x = r cos(?) and y = r sin(?) are used. This conversion is essential for determining the exact location of a point in a rectangular system.

Negative Angles in Polar Coordinates

Negative angles in polar coordinates indicate a clockwise rotation from the positive x-axis, as opposed to the standard counterclockwise rotation for positive angles. Understanding negative angles is crucial when converting polar coordinates to rectangular form.

Quadrant Determination

Once the rectangular coordinates are computed, the signs of the x and y values help determine which part of the coordinate plane the point lies in, whether it is in one of the quadrants or on one of the axes.

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