Identify whether the given equation is that of a cardioid, limaçon, rose, or lemniscate.
$r=1-\sin\theta$

• A. Cardioid
• B. Limacon
• C. Rose
• D. Lemniscate

Answer: (A)

Verified step by step guidance

1. Start by recognizing the general form of polar equations. The equation given is r = 1 - \sin\theta.
2. Understand the characteristics of different polar curves: Cardioids have the form r = a ± b\sin\theta or r = a ± b\cos\theta where a = b.
3. Compare the given equation r = 1 - \sin\theta with the standard form of a cardioid. Notice that it matches the form r = a - b\sin\theta with a = b = 1.
4. Recall that a cardioid is a special type of limaçon where the coefficients a and b are equal, resulting in a heart-shaped curve.
5. Conclude that the given equation r = 1 - \sin\theta represents a cardioid, based on its form and the equality of coefficients.