Convert the point to rectangular coordinates.
$(0,\frac{7\pi}{4})$

• A. $(0,\frac74)$
• B. $(-4,0)$
• C. $(0,0)$
• D. $(0,7)$

Answer: (C)

Verified step by step guidance

1. Identify the given point in polar coordinates: (r, θ) = (0, \frac{7\pi}{4}).
2. Recall the formulas to convert polar coordinates (r, θ) to rectangular coordinates (x, y): x = r \cos(θ) and y = r \sin(θ).
3. Substitute the given values into the formulas: x = 0 \cdot \cos(\frac{7\pi}{4}) and y = 0 \cdot \sin(\frac{7\pi}{4}).
4. Since the radius r is 0, both x and y will be 0 regardless of the angle θ.
5. Conclude that the rectangular coordinates are (x, y) = (0, 0).