Question

INSTANT FAN/MEDAL:
Determine the area of the inner loop of the polar curve r = 2 + 4 cos (θ).

Answer 1

\[2+4 \cos \theta =0,\cos \theta=-\frac{ 1 }{ 2 }=-\cos \frac{ \pi }{ 3 }=\cos \left( \pi-\frac{ \pi }{ 3 } \right),\cos \left( \pi+\frac{ \pi }{ 3 } \right)\]
\[\cos \theta=\cos \frac{ 2\pi }{ 3 },\cos \frac{ 4 \pi }{ 3 },\theta=\frac{ 2 \pi }{ 3 },\frac{ 4 \pi }{ 3 }\]
\[area=\int\limits_{\frac{ 2 \pi }{ 3 }}^{\frac{ 4 \pi }{ 3 }}\frac{ 1 }{ 2 }r^2 d \theta =?\]

Answer 2

is 5.055 the correct answer?

Answer 3

yes yes it is medal fan pls