## Angle Sum and Difference, Double Angle and Half Angle Formulas

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-SRT.A.2

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. These worksheets have students use a wide range of techniques to help them find the values of various different angles.

### Printable Worksheets And Lessons

- 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.

#### 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°)