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Multiple Choice
Convert the point to rectangular coordinates. (−2,−4π)
A
(2,−2)
B
(−1,1)
C
(−2,2)
D
(−22,22)
Verified step by step guidance
1
Step 1: Understand the problem. The given point (-2, -π/4) is in polar coordinates, where -2 is the radius (r) and -π/4 is the angle (θ) in radians. The goal is to convert this point into rectangular coordinates (x, y).
Step 2: Recall the formulas for converting polar coordinates to rectangular coordinates: x = r * cos(θ) and y = r * sin(θ). These formulas use the radius and angle to calculate the x and y components.
Step 3: Substitute the values of r and θ into the formulas. Here, r = -2 and θ = -π/4. For x, calculate x = -2 * cos(-π/4). For y, calculate y = -2 * sin(-π/4).
Step 4: Use trigonometric identities to simplify the calculations. Recall that cos(-θ) = cos(θ) and sin(-θ) = -sin(θ). Therefore, cos(-π/4) = cos(π/4) and sin(-π/4) = -sin(π/4).
Step 5: Evaluate the trigonometric values. From the unit circle, cos(π/4) = √2/2 and sin(π/4) = √2/2. Substitute these values into the equations for x and y. Simplify the expressions to find the rectangular coordinates.