Solve 20cos θ + 11 = 0

The given equation is:

$$20 \cos \theta + 11 = 0$$

Subtract 11 from both sides of the equation:

$$20 \cos \theta = -11$$

Divide both sides by 20:

$$\cos \theta = -\frac{11}{20}$$

To find $\theta$, we take the inverse cosine of $-\frac{11}{20}$. Let $\alpha = \arccos\left(-\frac{11}{20}\right)$.
The general solutions for $\cos \theta = k$ are given by:

$$\theta = 2n\pi \pm \alpha$$

where $n$ is an integer.

Substituting $\alpha = \arccos\left(-\frac{11}{20}\right)$:

$$\boxed{\theta = 2n\pi \pm \arccos\left(-\frac{11}{20}\right), \quad \text{where } n \in \mathbb{Z}}$$