# Space, shape and measurement: Solve problems by constructing and interpreting trigonometric models

### Subject outcome 3.6

Solve problems by constructing and interpreting geometrical models.

### Learning outcomes

• Define and use the following trigonometric functions: $\scriptsize \cos \theta$, $\scriptsize \sin \theta$, $\scriptsize \tan \theta$.
• Calculate trigonometric ratios in each of the quadrants where one ratio in that quadrant is given.
• Example: If $\scriptsize \sin \theta =\displaystyle \frac{3}{5}$ and $\scriptsize 90{}^\circ \le \theta \le 180{}^\circ$ determine $\scriptsize \cos \theta$.
• Solve problems in two dimensions using the trigonometric ratios $\scriptsize \cos \theta$, $\scriptsize \sin \theta$, $\scriptsize \tan \theta$.
• Express an appreciation of the contribution to the history of the development and the use of geometry and trigonometry by various cultures (NOT EXAMINABLE).

### Unit 1: Trigonometric ratios

By the end of this unit you will be able to:

• Define and use the trigonometric ratios of $\scriptsize \cos \theta$, $\scriptsize \sin \theta$ and $\scriptsize \tan \theta$.
• Calculate the trigonometric ratios in each quadrant of the Cartesian plane.
• Calculate the value of expressions containing trigonometric ratios.

### Unit outcomes: Unit 2: Problems in two dimensions (2D)

By the end of this unit you will be able to:

• Use a calculator to calculate the value of the three basic trig ratios for different angles.
• Solve problems in two dimensions (2D) using the trigonometric ratios $\scriptsize \cos \theta$, $\scriptsize \sin \theta$, $\scriptsize \tan \theta$.