The rectangular coordinates of a point are given. Find polar coordinates for the point.

Question

The rectangular coordinates of a point are given. Find polar coordinates for the point. (Enter your answer using r > 0 and 0 ≤ θ < 2π. Round your answers to two decimal places.)
(1.3, -2.3)

 

 

Please help!!!

Answer 1

The polar coordinates of the point are (r, θ), where r is the distance from (0,0) to (1.3, -2.3) and θ is the angle measured counterclockwise with vertex (0, 0), initial side the positive x-axis, and terminal side the ray with endpoint (0,0) and which passes through the point (1.3, -2.3).  

 

r = √([1.3 - 0]² + [-2.3 - 0]²) = √6.98 ≈ 2.64

 

tan^-1(2.3/1.3) ≈ 1.056

 

So, since the given point lies in quadrant 4, θ = 2π - 1.056

                                                                               = 5.23                                                                                         

Polar coordinates of (1.3, -2.3) are (2.64, 5.23)