Convert the point to rectangular coordinates.
$(-2,-\frac{\pi}{4})$

• A. $(\sqrt{2},-\sqrt2)$
• B. $(-1,1)$
• C. $(-\sqrt{2},\sqrt{2})$
• D. $(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$

Answer: (C)

Verified step by step guidance

1. Identify the given polar coordinates: (r, θ) = (-2, -\frac{\pi}{4}).
2. Recall the formulas to convert polar coordinates to rectangular coordinates: x = r \cdot \cos(θ) and y = r \cdot \sin(θ).
3. Substitute the given values into the formulas: x = -2 \cdot \cos(-\frac{\pi}{4}) and y = -2 \cdot \sin(-\frac{\pi}{4}).
4. Calculate \cos(-\frac{\pi}{4}) and \sin(-\frac{\pi}{4}). Remember that \cos(-θ) = \cos(θ) and \sin(-θ) = -\sin(θ).
5. Simplify the expressions to find the rectangular coordinates (x, y).