Half angle formulas are super helpful when we want to solve problems with angles in trigonometry.

These formulas break down tricky angles into simpler parts.

For example, they help us figure out functions like

• $\sin\left(\frac{\theta}{2}\right)$
• or $\cos\left(\frac{\theta}{2}\right)$.

When we use these formulas, it makes our math calculations much easier.

Let’s say you want to find $\sin\left(\frac{30^\circ}{2}\right)$.

You can use the half angle formula:

$\sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1 - \cos(\theta)}{2}}.$

This makes the problem simpler to solve!

These formulas are also great for integration and solving other equations with trigonometric identities.

That's why they are very important tools in pre-calculus!