Find the rectangular coordinates of (7,30°).

To convert from polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:

x = r * cos(θ)
y = r * sin(θ)

In this case, the polar coordinates are (7, 30°). To find the rectangular coordinates, plug these values into the formulas:

x = 7 * cos(30°)
y = 7 * sin(30°)

To evaluate these trigonometric functions, you need to convert the angle from degrees to radians. Since π radians is equal to 180 degrees, you can use the conversion factor:

1° = π/180 radians

Now, plug in the values and calculate:

x = 7 * cos(30° * π/180)
y = 7 * sin(30° * π/180)

Simplify:

x = 7 * cos(π/6)
y = 7 * sin(π/6)

Evaluate the trigonometric functions:

x = 7 * √3 / 2
y = 7 * 1/2

Simplify further:

x = 7√3 / 2
y = 7/2

Therefore, the rectangular coordinates are (7√3 / 2, 7/2).