📘 polar coordinates

1. The problem asks to graph the polar curve given by the equation $\theta = 0$. 2. In polar coordinates, $\theta$ represents the angle from the positive x-axis (polar axis).

1. **State the problem:** We need to graph the polar curve given by the equation $$r = -3 - 5 \cos \theta$$. 2. **Identify the type of curve:** This is a limaçon curve because it h

1. **Problem Statement:** Graph the polar curve given by $$r = -3 - 5 \cos \theta$$. 2. **Understanding the Curve Type:** This is a limaçon curve of the form $$r = a + b \cos \thet

1. **Problem:** Identify the type of graph for the polar equation $$r^2 = 9 \cos 2\theta$$. 2. **Formula and rules:**

1. **State the problem:** Identify the symmetries of the polar curve $$r = \sin\left(\frac{\theta}{2}\right)$$ and then sketch it. 2. **Recall symmetry types for polar curves:**

1. Problem Q3: Convert Cartesian equations to polar coordinates using formulas $x = r\cos\theta$ and $y = r\sin\theta$. (a) Given $\frac{x^2}{9} + \frac{y^2}{4} = 1$.