Convert to Rectangular Coordinates (-1,pi/2)

Problem

(−1,π/2)

Solution

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

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

3. Substitute the values into the x equation:

x=−1*cos(π/2)

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

x=−1*(0)=0

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

6. Substitute the values into the y equation:

y=−1*sin(π/2)

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

y=−1*(1)=−1

Final Answer

(r,θ)=(−1,π/2)⇒(x,y)=(0,−1)

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