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

Problem

(−4,π/2)

Solution

1. Identify the given polar coordinates (r,θ) where r=−4 and θ=π/2

2. Apply the formula for the xcoordinate using x=r*cos(θ)

x=−4*cos(π/2)

3. Evaluate the cosine function, noting that cos(π/2)=0

x=−4*(0)=0

4. Apply the formula for the ycoordinate using y=r*sin(θ)

y=−4*sin(π/2)

5. Evaluate the sine function, noting that sin(π/2)=1

y=−4*(1)=−4

Final Answer

(−4,π/2)=(0,−4)

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