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

• A. $(\(\sqrt{2}\),-\(\sqrt\)2)$
• 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. Understand that the given point is in polar coordinates, which are represented as (r, θ), where r is the radius and θ is the angle.
2. To convert polar coordinates to rectangular coordinates (x, y), use the formulas: x = r * cos(θ) and y = r * sin(θ).
3. For the point (-2, -π/4), substitute r = -2 and θ = -π/4 into the formulas: x = -2 * cos(-π/4) and y = -2 * sin(-π/4).
4. Calculate cos(-π/4) and sin(-π/4). Remember that cos(-θ) = cos(θ) and sin(-θ) = -sin(θ). Therefore, cos(-π/4) = cos(π/4) = √2/2 and sin(-π/4) = -sin(π/4) = -√2/2.
5. Substitute these values into the equations: x = -2 * (√2/2) and y = -2 * (-√2/2), and simplify to find the rectangular coordinates.