# Compound Angle Formulae

## Understanding Compound Angle Formulae

**Definition and Importance of Compound Angles**

- Acknowledge what
**compound angles**are and their significance in trigonometry. - Recognise the inherent blend of algebra and trigonometry in these formulae, leading to useful values of sine, cosine, and tangent.

**Mastering the Basic Compound Angle Formulae**

- Familiarise with the basic compound angle formulae for sine, cosine and tangent: sin(A ± B), cos(A ± B), and tan(A ± B).
- Demonstrate ability to derive these formulae if required, using core trigonometric properties and identities.

**Applying Compound Angle Formulae**

- Gain proficiency in using these formulae to simplify trigonometric expressions or solve equations.
- Infer that because these formulae involve two angles, they have wide-ranging applications in mathematics, including complex numbers and analytic geometry.

## Range of Applications

**Compound Angle Formulae in Trigonometric Identities**

- Comprehend the use of compound angle formulae in proof and derivation of further trigonometric identities.
- Note the role they play in the proofs of double-angle and half-angle identities.

**Use in Exact Trigonometric Values**

- Understand their application in derivation of exact trigonometric values for the angles 15°, 30°, 45°, 60° and 90°.
- Be capable of obtaining exact values for other angles using these formulae.

**Utility in Trigonometric Equations**

- Respect the utility of compound angle formulae in solving trigonometric equations.
- Be familiar with techniques for tackling an equation which involves the sum or difference of two angles.

**Real-world Applications**

- Appreciate the practical applications of compound angle formulae in physics and geometry.
- Be aware that they often provide solutions or simplifications in problems involving circles, waves, oscillation, and vectors.

**Connection with Complex Numbers and De Moivre’s Theorem**

- Notice the connection between compound angle formulae and the geometry and arithmetic of complex numbers.
- Be versed in how they help in the proof and application of
**De Moivre’s Theorem**. - Understand their application in finding the nth roots of complex numbers.

**Use in Analytic Geometry**

- Understand the use of compound angle formulae in finding the equation of a line, circle, or parabola in the complex plane.
- Appreciate their service in solving problems of rotation and translation in the plane.