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).