Final answer:
To convert the Cartesian coordinate (2,6) to polar coordinates, calculate r = √40 = 2√10 and θ = arctan(3). The point in polar coordinates is (2√10, arctan(3)).
Step-by-step explanation:
To convert the Cartesian coordinate (2,6) to polar coordinates, we need to find the radial distance r and the angle θ, where 0 ≤ θ < 2π.
The radial distance r can be found using the Pythagorean theorem: r = √(x² + y²).
In this case, r = √(2² + 6²) = √(4+36) = √40 = 2√10. To find the angle θ, we take the arctangent of the y-coordinate divided by the x-coordinate, θ = arctan(y/x). Therefore, θ = arctan(6/2) = arctan(3).
Since the point (2,6) is in the first quadrant where both x and y are positive, θ = arctan(3) is the correct angle and no further adjustments are needed.
Converting to polar coordinates, the point (2,6) is represented as (2√10, arctan(3)) with θ expressed in radians.