Final answer:
The Cartesian coordinates for the polar coordinates (3, π/6) are (1.5√3, 1.5) using the conversion formulas x = r * cos(θ) and y = r * sin(θ).
Step-by-step explanation:
The student asked what are the Cartesian coordinates of the point of polar coordinates (3, π/6). To find the Cartesian coordinates from polar coordinates, we use the equations x = r * cos(θ) and y = r * sin(θ), where r is the radial distance from the origin and θ is the angle in radians from the positive x-axis.
For the given polar coordinates (3, π/6), we calculate the Cartesian coordinates as follows:
- x = 3 * cos(π/6) = 3 * √3/2 = 1.5 √3
- y = 3 * sin(π/6) = 3 * 1/2 = 1.5
Therefore, the Cartesian coordinates corresponding to the polar coordinates (3, π/6) are (1.5 √3, 1.5).