Write the polar equation in rectangular form r=-12 sinè
You should know that
r^2 = x^2 + y^2 and sinØ = y/r
so in r = - 12sinØ
r = -12y/r
r^2 = -12y
x^2 + y^2 = -12y
x^2+y^2-4x-12y+31=0
To convert the polar equation r = -12sin(θ) to rectangular form, we can use the trigonometric identities:
x = r*cos(θ)
y = r*sin(θ)
Substituting in the given equation:
x = -12sin(θ)*cos(θ)
y = -12sin^2(θ)
Next, we can use the double-angle identities to simplify the expressions:
x = -6sin(2θ)
y = -6(1 - cos(2θ))/2
Finally, we can rewrite the rectangular form:
x = -6sin(2θ)
y = 3cos(2θ) - 3
So, the rectangular form of the polar equation r = -12sin(θ) is x = -6sin(2θ) and y = 3cos(2θ) - 3.