Final answer:
The polar coordinates (7, 45°) can be converted to rectangular coordinates by using the formulas x = r * cos(θ) and y = r * sin(θ). The correct rectangular coordinates are (7√2/2, 7√2/2).
Step-by-step explanation:
To convert the polar coordinates (7, 45°) to rectangular coordinates, you can use the sine and cosine trigonometric functions, as the rectangular coordinates (x, y) can be found using the formulas x = r * cos(θ) and y = r * sin(θ) where r is the radius and θ is the angle in degrees.
To convert (7, 45°) to rectangular coordinates, we can use the formulas x = r * cos(θ) and y = r * sin(θ), where r is the magnitude (7) and θ is the angle (45°).
Plugging in the values, we get x = 7 * cos(45°) = 7 * (√2/2) = 7√2/2, and y = 7 * sin(45°) = 7 * (√2/2) = 7√2/2.
Therefore, the rectangular coordinates are (7√2/2, 7√2/2). So, the correct answer is C) (7√2/2, 7√2/2).
In this case, for r = 7 and θ = 45°:
- x = 7 * cos(45°) = 7 * √2/2
- y = 7 * sin(45°) = 7 * √2/2
Therefore, the rectangular coordinates are (7√2/2, 7√2/2), which corresponds to choice C.