r 0 r Solutionusing pythagoras theorem r2 122 sqrt

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Solution

using pythagoras theorem

r^2 = (-12)^2 + (sqrt 3)^2

r^2 = 144 + 3 = 147

r = sqrt (147 )

theta = tan^-1 ( y/x) = tan^-1 ( sqrt 3 / -12) = 3

subtracting the angle from 2pi = 3.28

r > 0 (r,theta ) = sqrt 147 , 3.28

for r < 0

3.28 - pi = sqrt 147 , .14