Convert to Polar Coordinates (7,-7)

Problem

(7,−7)

Solution

1. Identify the Cartesian coordinates (x,y) where x=7 and y=−7

2. Calculate the radial distance r using the formula r=√(,x^2+y^2)

r=√(,7^2+(−7)^2)

r=√(,49+49)

r=√(,98)

r=7√(,2)

3. Determine the reference angle θ^′ using the formula tan(θ^′)=|y/x|

tan(θ^′)=|(−7)/7|

tan(θ^′)=1

θ^′=π/4

4. Find the actual angle θ by observing that the point (7,−7) lies in Quadrant IV.

θ=2*π−π/4

θ=(7*π)/4

Final Answer

(7,−7)=(7√(,2),(7*π)/4)

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