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

Expand the square

Substitute  

r

2

for  

x

2

+

y

2

and  

r

sin

(

θ

)

for y

Combine like terms

Divide both sides by r

Express r in terms of  

θ

Explanation:

Expand the square:

y

2

−

4

y

+

4

+

x

2

=

4

Substitute  

r

2

for  

x

2

+

y

2

and  

r

cos

(

θ

)

for y:

r

2

−

4

r

sin

(

θ

)

+

4

=

4

Combine like terms:

r

2

−

4

r

sin

(

θ

)

=

0

Divided both sides by r:

r

−

4

sin

(

θ

)

=

0

Express r in terms of theta:

r

=

4

sin

(

θ

)

80

step-by-step explanation: