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

Problem

(−2,π/4)

Solution

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

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

x=−2*cos(π/4)

3. Evaluate the cosine of π/4 which is √(,2)/2

x=−2⋅√(,2)/2=−√(,2)

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

y=−2*sin(π/4)

5. Evaluate the sine of π/4 which is √(,2)/2

y=−2⋅√(,2)/2=−√(,2)

Final Answer

(r,θ)=(−2,π/4)⇒(x,y)=(−√(,2),−√(,2))

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