Find the rectangular coordinates of (7, 30°)
to convert,
x = rcosØ, and y = rsinØ
so the point is
(7cos30°, 7sin30°)
= (7√3/2, 7/2
To find the rectangular coordinates of a point given in polar coordinates, we can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
In this case, the point is given as (7, 30°), where 7 is the distance from the origin (r) and 30° is the angle (theta) measured from the positive x-axis.
Now, applying the formulas:
x = 7 * cos(30°)
y = 7 * sin(30°)
To calculate the values, we need to convert 30° to radians, since the trigonometric functions in most programming languages and calculators expect angles in radians.
Converting 30° to radians:
theta (in radians) = (30° * π) / 180°
theta (in radians) = π / 6
Substituting the values:
x = 7 * cos(π / 6)
y = 7 * sin(π / 6)
Evaluating the trigonometric functions:
x ≈ 7 * 0.866
y ≈ 7 * 0.5
Calculating the values:
x ≈ 6.06
y ≈ 3.5
Therefore, the rectangular coordinates of (7, 30°) are approximately (6.06, 3.5).