the polar coordinates (2, π/3) to rectangular coordinates:
Plotting the Point:
Understand Polar Coordinates:
Polar coordinates are represented as a pair of values:
r: the distance from the origin (polar axis)
θ: the angle between the positive x-axis and the line connecting the origin and the point.
Extract Values:
From the given coordinates, we have:
r = 2 (distance)
θ = π/3 (angle)
Calculate X and Y components:
In rectangular coordinates, the point is represented by (x, y).
We can use the following formulas to convert polar coordinates to rectangular:
x = r * cos(θ)
y = r * sin(θ)
Substitute values and calculate:
x = 2 * cos(π/3) = 2 * (1/2) = 1
y = 2 * sin(π/3) = 2 * (√3/2) = √3
Plot the Point:
Using the calculated x and y values (1, √3), plot the point on a graph with x-axis and y-axis.
Converting to Rectangular Coordinates:
Read the Point:
From the graph, we can read the coordinates of the plotted point as:
x = 1
y = √3
Therefore, the rectangular coordinates of the point (2, π/3) are (1, √3).
The graph plotted in the previous step visually confirms this conversion.