Question

Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3,-2) $$

Short answer

The polar coordinates for the point (3, -2) in rectangular coordinates are √13 and 326.3°.

Step-by-step solution

Calculating Radius

Calculate r using the formula \(r = √(x² + y²)\). Substituting x=3 and y=-2, we get \(r = √((3)² +(-2)²)=√(9+4)=√13.\)

Calculating Angle using Graphing Tool

Use a graphing utility to calculate θ using the atan2 (y, x) function. This function gives the angle θ in the right quadrant. Note that the atan2 function is particularly useful over other arctan functions because it preserves the quadrant of the point. Substituting y = -2 and x = 3 in atan2 function, the graphing utility gives θ around -33.7 degrees.

Adjusting for Polar Coordinates

If the angle θ is negative, add 360° to get the angle in polar coordinates. Hence, θ = -33.7° + 360° = 326.3°.