Convert to Polar Coordinates (-4,-pi/2)

Problem

(−4,−π/2)

Solution

1. Identify the given coordinates as polar coordinates (r,θ) where r=−4 and θ=−π/2 The task is to find an equivalent representation, typically with a positive radius r>0

2. Apply the rule for a negative radius, which states that the point (−r,θ) is equivalent to (r,θ+π)

3. Substitute the values into the formula to find the new radius.

r=−(−4)

r=4

4. Calculate the new angle by adding π to the original angle.

(θ_new)=−π/2+π

(θ_new)=π/2

5. Verify the point on the Cartesian plane. The original point (−4,−π/2) means moving in the opposite direction of −π/2 (which is the negative y-axis) by 4 units, landing on the positive y-axis at (0,4) The coordinate (4,π/2) also represents (0,4)

Final Answer

(−4,−π/2)=(4,π/2)

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