In Exercises 15-22, use an algebraic method to find the...

In Exercises $15-22,$ use an algebraic method to find the rectangular coordinates of the point with given polar coordinates. Approximate the exact solution values with a calculator when appropriate.
$$
\left(-3,360^{\circ}\right)
$$

Key Concepts

Polar Coordinates

Polar coordinates represent points in the plane using a distance from the origin and an angle from the positive x-axis. This system is particularly useful for problems involving circular or rotational symmetry, and it uses a pair (r, ?) where r is the radius (which can be negative, indicating a point in the opposite direction of the angle) and ? is the angle measured in degrees or radians.

Rectangular Coordinates

Rectangular coordinates (or Cartesian coordinates) describe the location of a point using two values that correspond to its horizontal (x) and vertical (y) distances from the origin. This coordinate system is widely used in algebra and calculus due to its straightforward application in linear equations and geometric constructions.

Conversion Formulas

The conversion between polar and rectangular coordinates is accomplished using trigonometric functions. Given polar coordinates (r, ?), the rectangular coordinates can be found using the formulas x = r cos ? and y = r sin ?. These formulas embody the connection between the geometric interpretation of a point defined by an angle and radius and its projection onto the x and y axes.

Trigonometric Functions

Trigonometric functions such as sine and cosine are used in the conversion process to relate an angle to ratios of side lengths in a right triangle. In the context of converting coordinates, these functions allow for the calculation of the x and y components from the radius and angle, illustrating the intersection between geometry and algebra.

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