Convert to Rectangular Coordinates (-1,270)

Problem

(r,θ)=(−1,270)

Solution

1. Identify the given polar coordinates where r=−1 and θ=270

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

3. Substitute the values into the x equation:

x=−1⋅cos(270)

4. Evaluate the cosine of 270 which is 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(270)

7. Evaluate the sine of 270 which is −1

y=−1⋅(−1)=1

Final Answer

(x,y)=(0,1)

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