## What are double angle formulas used for?

The double-angle formulas can be used to derive the reduction formulas, which are formulas we can use to reduce the power of a given expression involving even powers of sine or cosine. They allow us to rewrite the even powers of sine or cosine in terms of the first power of cosine.

## Why are double angle identities important?

**How do you read double angle formulas?**

The cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ. For example, cos(60) is equal to cos²(30)-sin²(30).

### What is the power reducing formula?

The power-reducing formula is an identity useful in rewriting trigonometric functions raised to powers. These identities are rearranged double-angle identities that function much like the double-angle and half-angle formulas.

### What are half angle identities used for?

You can use half-angle identities to evaluate a trig function of an angle that isn’t on the unit circle by using one that is. For example, 15 degrees, which isn’t on the unit circle, is half of 30 degrees, which is on the unit circle.

**When to use half angle and reduction formulas?**

The next set of identities is the set of half-angle formulas, which can be derived from the reduction formulas and we can use when we have an angle that is half the size of a special angle. If we replace θ with α 2, the half-angle formula for sine is found by simplifying the equation and solving for sin(α 2).

## How to find the formula for double angle?

First, starting from the sum formula, cos(α + β) = cosα cosβ − sinα sin β, and letting α = β = θ, we have Using the Pythagorean properties, we can expand this double-angle formula for cosine and get two more interpretations.

## How to find the half angle formula for sine?

If we replace θ with α 2, the half-angle formula for sine is found by simplifying the equation and solving for sin(α 2). Note that the half-angle formulas are preceded by a ± sign. This does not mean that both the positive and negative expressions are valid. Rather, it depends on the quadrant in which α 2 terminates.

**How are double angle and half angle identities derived?**

Double-angle identities are derived from the sum formulas of the fundamental trigonometric functions: sine, cosine, and tangent. See (Figure), (Figure), (Figure), and (Figure). Reduction formulas are especially useful in calculus, as they allow us to reduce the power of the trigonometric term. See (Figure) and (Figure).