/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 15 Use the angle feature of a graph... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

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

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

Step by step solution

01

Calculating Radius

Calculate r using the formula \(r = √(x² + y²)\). Substituting x=3 and y=-2, we get \(r = √((3)² +(-2)²)=√(9+4)=√13.\)
02

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.
03

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°.

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