# Double Angle and Half Angle Identities Worksheets

We cover a wide series of skills on this page. Some of them will help you learn to evaluate special circumstances in trigonometric identities. Others will focus on simplifying the expressions and equations that we will use to do this type of work. We also look at situations where you will be working with angle sums and differences and how to process those types of problems. These worksheets have students use a wide range of techniques to help them find the values of various different angles.

### Aligned Standard: HSG-SRT.A.2

- Differences Step-by-Step Lesson- Find the difference between the sin and cos value of angles.
- Guided Lesson - Everything on this topic in one. Three questions that all target a different skill.
- Guided Lesson Explanation - Sorry if you are thrown off by the lack of space between sin/cos and the angle. That is a habit to remind students to factor that value in first.
- Practice Worksheet - A nice mix for you to work with. It makes it very interesting to work on these.
- Matching Worksheet - Match the final value of all the operations and value shifts.
- Angle Sum and Difference, Double Angle and Half Angle Formulas Five Pack of Worksheets - Ten problems can take you a good amount of time.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Going over the steps with the kids should really help a great deal.

- Homework 1 - Formula: Sin A Cos B – Cos A Sin B = Sin (A - B)
- Homework 2 - If sin x = 1/2, find cos (2 x)
- Homework 3 - Formula: Cos A Cos B – Sin A Sin B = Cos (A+B)

### Practice Worksheets

These are all broken down into step based answers too.

- Practice 1 - Find the exact value of: cos 90° cos 60° - sin 90° sin 60°
- Practice 2 - If sin x = 5/8, find Cos (2 x)
- Practice 3 - Sin 90° cos 30° + Cos 90° sin 30°= Sin (120°)

### Math Skill Quizzes

Some these questions will be extremely easy and some will be the inverse of that.

- Quiz 1 - Find the exact value of Cos 60°
- Quiz 2 - Find the exact value of cos 45° sin45° + Cos 45° sin45°
- Quiz 3 - What is the cost of a zero angle? Ask problem number seven.

### What are Double Angle and Half Angle Identities?

They arise in specials circumstances where you were processing a sum or difference for sine and/or cosine. Let’s say for instance if you were working with the equation: sin (x + y) = (sin x)(cos y) + (cos x)(sin y), when you process this and replace y with x, you are left with the double angle identity for sine: sin 2x = 2 sin x cos x. Once we identify it as such, to make sense of it we just use the formula outlined below. The alternative form of this is called half angle identities. The math is similar, just flipped upside down. For instance, if you were working with: cos 2x = 1 – 2 sin^{2} x. When we process this out we will end up with: sin x/2 = ± √ [(1 – cos x)/2].

### What is the Double Angle Formula?

This is a trigonometric identity that express 2 Θ in terms of the trigonometric function of Θ. We will use it to solve special circumstances where we can identify a double angle.

### What is the Half Angle Formula?

There are instances where we know the actual value of the trigonometric functions for the half angles. For example, by using these formulas, we can easily transform any expression that has exponents to something without exponents, but its angles are multiples of its original.

Not many people know but half-angle formulas from the double angle formulas. Both Sin (2A) and Cos (2A) are basically derived from the same angle formula for cosine.

cos (2A) = cos2(A) - sin2(A) = cos2(A) - (1 - cos 2A) = 2cos 2(A) – 1. So, cos^{2} (A) = (1 + cos (2A) / 2) . If we replace A by (1/2)A and take its square root we will be getting Cos (a/2) = ± √ (1 + cos (A))/2

In the same way, we can compose the sine half angler.