Convert to Rectangular Coordinates (5,(3pi)/4)

Problem

(5,(3*π)/4)

Solution

1. Identify the given polar coordinates (r,θ) where r=5 and θ=(3*π)/4

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

x=5*cos((3*π)/4)

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

x=5*(−√(,2)/2)=−(5√(,2))/2

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

y=5*sin((3*π)/4)

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

y=5*(√(,2)/2)=(5√(,2))/2

Final Answer

(5,(3*π)/4)=(−(5√(,2))/2,(5√(,2))/2)

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