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CSS Pure Mathematics QUESTION #4133
Question 1
What is the area enclosed by the polar curve $r = 2\cos(\theta)$?
  • $\pi$✔️
  • $2\pi$
  • $4\pi$
  • $\frac{\pi}{2}$
Correct Answer Explanation
Circle with radius $1$ has area $\pi(1)^2 = \pi$. Or by integration: $A = \frac{1}{2} \int_{-\pi/2}^{\pi/2} (2\cos(\theta))^2 d\theta = 2\int_{-\pi/2}^{\pi/2} \cos^2(\theta) d\theta = \pi$.