Trigonometric Functions

This module of Maths Extension 1 explores some advanced applications of trigonometric functions to solve more complex problems. Trigonometric functions provide an algebraic representation of geometric problems, and by being able to construct algebraic identities to simplify or modify expressions that contain these we will be able to solve interesting problems in geometry.

What You'll Learn

Calculating exact trigonmetric functions for new angles

In this topic, you will learn how to work with expressions that combine addition or subtraction and trigonometric functions like sine, cosine and tangent.

• The compound angle formulae for sums
• The compound angle formulae for differences

Solving equations involving multiple periodic functions

You will also learn how multiple trigonometric functions with the same period can be consolidated into a single trigonometric function and use this to find the solutions to equations like

$$5\sin\theta + 12\cos\theta = 13$$

• Combining trigonometric sums

Simplifying expressions involving multiple trigonometric functions

You will also learn how to use the trigonometric identities you know to verify the correctness of new equalities, and how these can be applied to greatly simplify expressions involving trigonometric equations. Combined with skills in the calculus module, you will learn how this can be used to perform more advanced integration such as

$$\int\frac1{sin\theta}d\theta$$

• Proving Trigonometric Identities
• The t-Formulae for Trigonometric Functions

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