Problem 15
Question
Use the angle feature of a graphing utility to find one set of polar coordinates for the point given in rectangular coordinates. $$ (3,-2) $$
Step-by-Step Solution
Verified Answer
The polar coordinates for the point (3, -2) in rectangular coordinates are √13 and 326.3°.
1Step 1: Calculating Radius
Calculate r using the formula \(r = √(x² + y²)\). Substituting x=3 and y=-2, we get \(r = √((3)² +(-2)²)=√(9+4)=√13.\)
2Step 2: 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.
3Step 3: 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°.
Other exercises in this chapter
Problem 15
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