# Trig. Functions

## Trig. Functions

**Trigonometric Functions**

## Definitions and Basic Concepts

- Gain a strong understanding of trigonometric
**functions**including, but not limited to,**sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)**. - Learn to identify and create
**periodic functions**, which are functions that repeat their values in regular intervals. - Develop an appreciation for the relationship between
**radians and degrees**, and understand how to convert between the two.

## Trigonometric Identities

- Learn to recognise and apply more complex trigonometric identities, such as the
**product-to-sum and sum-to-product identities**. - Understand how to use the
**cofunction identities (sin(π/2 - θ) = cos θ), etc.**, to enable simplification of expressions and solutions to problems.

## Inverse Trigonometric Functions

- Familiarise yourself with the concept of
**inverse trigonometric functions (sin⁻¹, cos⁻¹, tan⁻¹ etc.)**and their respective domains and ranges. - Apply your knowledge of these inverse functions to solve complex problems and evaluate unknown quantities.
- Understand the relationship between a function and its inverse, especially focusing on the
**sin x function and its inverse**.

## Graphs of Trigonometric Functions

- Understand how trigonometric functions can be transformed, and how these transformations can affect their
**graphs**. - Issues to consider include
**amplitude, period, phase shift**, as well as horizontal and vertical transformations. - Draw and interpret graphs of
**csc, sec, and cot**, in addition to sin, cos, and tan. Identify behaviours such as asymptotes and points of inflection. - Recognise the impact of domain restrictions on the graph of inverse trigonometric functions.

## Solving Trigonometric Problems

- Master techniques to solve more complex trigonometric problems, such as those involving
**multiple angles or periodic functions**. - Use your understanding of
**inverse trigonometric functions**to solve equations, and your knowledge of**identities**to simplify expressions and prove equivalences. - Understand and apply the principle of the
**compound angle formula**to break down more complex problems into simpler ones.