Convert to Polar Coordinates (2,(5pi)/4)

Problem

(2,(5*π)/4)

Solution

1. Identify the given coordinates as polar coordinates (r,θ) where r=2 and θ=(5*π)/4

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

x=2*cos((5*π)/4)

3. Evaluate the cosine of (5*π)/4 which is −√(,2)/2

x=2*(−√(,2)/2)

x=−√(,2)

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

y=2*sin((5*π)/4)

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

y=2*(−√(,2)/2)

y=−√(,2)

Final Answer

(2,(5*π)/4)=(−√(,2),−√(,2))

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