Solve `(dr)/(d theta)= cos theta`.

Answer

To solve the differential equation \(\frac{dr}{d\theta} = \cos \theta\), we will follow these steps:

### Step 1: Separate the Variables
We start with the given equation:
\[ \frac{dr}{d\theta} = \cos \theta \]
We can separate the variables by multiplying both sides by \(d\theta\):
\[ dr = \cos \theta \, d\theta \]

### Step 2: Integrate Both Sides
Next, we will integrate both sides. The left side integrates with respect to \(r\) and the right side integrates with respect to \(\theta\):
\[ \int dr = \int \cos \theta \, d\theta \]
The integral of \(dr\) is simply \(r\). The integral of \(\cos \theta\) is \(\sin \theta\):
\[ r = \sin \theta + C \]
where \(C\) is the constant of integration.

### Final Solution
Thus, the solution to the differential equation is:
\[ r = \sin \theta + C \]