Convert the rectangular equation to a polar equation that ex

Convert the rectangular equation to a polar equation that expresses r in terms of theta. x^2 + (y + 2)^2 = 4 r = (Type an expression in terms of theta.)

Solution

Solution:

to convert into polar coordinate

plug x = rcos()

y = rsin()

x²+ (y+2)² = 4

(r cos())² + (rsin() +2 )² = 4

r² cos²() + r²sin²() + 2rsin() +4 = 4

r² (  cos²() + sin²() ) + 2 r sin() = 0

r² + 2rsin() =0

r = 0

r = - 2sin()

r =0 is not possible

therefore

Answer: r = -2sin()