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Angle Sum and Difference, Double Angle and Half Angle Formulas

HSG-SRT.A.2
Answer Keys Here

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, cos2 (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




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.