Convert to Rectangular Coordinates (4,(3pi)/2)

Problem

(4,(3*π)/2)

Solution

1. Identify the polar coordinates (r,θ) where r=4 and θ=(3*π)/2

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

3. Substitute the values into the x equation: x=4*cos((3*π)/2)

4. Evaluate the cosine function: since cos((3*π)/2)=0 then x=4*(0)=0

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

6. Substitute the values into the y equation: y=4*sin((3*π)/2)

7. Evaluate the sine function: since sin((3*π)/2)=−1 then y=4*(−1)=−4

Final Answer

(4,(3*π)/2)=(0,−4)

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