# Equations

## Equations in Trigonometry

**Solving Trigonometric Equations**

- Understand the approaches for solving simple trigonometric equations for
**radians**and**degrees**within a given domain. - Be equipped to solve equations involving multiple angles, such as sin(2x) or cos(3x).
- Get comfortable with the methodology used for solving equations involving trigonometric identities, with emphasis on
**exact value solutions**. - Appreciate that the solution of such equations may yield
**extraneous roots**which fall outside the prescribed domain.

**Manipulation of Trigonometric Equations**

- Develop adeptness in the manipulation of trigonometric equations involving
**sums**and**differences**of angles. - Be familiar with the process of transforming an equation by use of
**double**,**half-angle**or**angle sum and difference**formulas. - Be able to apply these transformation techniques in order to find
**solutions to trigonometric equations**, or**simplify the equations**themselves. - Master the art of
**factorising or expanding**trigonometric expressions where appropriate.

**Trigonometric Solutions in Real World Modelling**

- Apply the principles of solving trigonometric equations in the context of
**real-world modelling problems**, such as wave function, harmonic motions or periodic phenomena like sound or light waves. - Be familiar with the notation used in such contexts, and be able to sketch and interpret
**trigonometric functions**representing these models.

**Graphical Understanding of Trigonometric Equations**

- Learn to associate solutions of trigonometric equations with geometric properties, such as
**intersections of a circle**with a line. - Relate the root finding problem in trigonometric equations to the corresponding situation on the
**graph of y = sinx**,**y = cosx**or**y = tanx**. - Understand the role the
**unit circle**plays in solving trigonometric equations, and be able to find solutions using this method.