Question

The asymptote of the spiral \( r = \frac{\theta}{\sin \theta} \) is:

• A. \( r \sin \theta = \alpha \)
• B. \( r \sin \theta + \alpha + 1 = 0 \)
• C. \( r \cos \theta = \alpha \)
• D. \( a \sin \theta = 2r \)

Hint:

In polar coordinates, the asymptote of a spiral can be found by analyzing its behavior at large values of θ.

Answer 1

The Correct Option is A

The spiral \( r = \frac{\theta}{\sin \theta} \) asymptotically approaches a straight line, and its asymptote is given by the relation \( r \sin \theta = \alpha \).