for the point with cartesioan coordiantes (5,-2) find polar coordinated such that r>0. express it in radians. so far i got the answer to be -.38805...is dat the answer or should i add 2pie or 360 to get r>0?
Add 2PI
but it says to radians?
Apologies for the confusion. When finding the polar coordinates in radians, we need to specify the angle between 0 and 2π (or 0 and 360 degrees).
To convert Cartesian coordinates to polar coordinates, we use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
For the point (5, -2):
r = √(5^2 + (-2)^2) = √(25 + 4) = √29
To find θ, we can use the arctan function. Since the point is in the second quadrant (negative x and y values), we need to add π or 180 degrees to the angle obtained from arctan.
θ = arctan(-2/5) + π
θ ≈ -0.380506 + π
θ ≈ 2.761791 radians
So the polar coordinates (r, θ) in radians are approximately (√29, 2.761791).