Convert to Rectangular Coordinates (-3,(-pi)/2)

Problem

(r,θ)=(−3,−π/2)

Solution

1. Identify the polar coordinates (r,θ) where r=−3 and θ=−π/2

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

x=−3*cos(−π/2)

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

x=−3*(0)=0

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

y=−3*sin(−π/2)

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

y=−3*(−1)=3

Final Answer

(r,θ)=(−3,−π/2)⇒(x,y)=(0,3)

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