# SACE Stage 1 Mathematics – Vectors in the Plane and Further Trigonometry

5.1 Vector Operations
5.2 Component and Unit Vector Forms
5.3 Projections
5.4 Geometric Proofs using Vectors
5.5 Further Trigonometric Functions
5.6 Trigonometric Identities

## Vectors in the Plane

Studying vectors in the plane provides new perspectives for working with two-dimensional space. Vectors are used to specify quantities that have size (magnitude) and direction. These quantities include velocity, force, acceleration, and displacement and are used in fields such as physics and engineering. The topic includes vector operations, their applications, and their use in proving results in geometry.

## Further Trigonometry

In this topic, students extend their understanding of trigonometric functions. Students model circular motion in the familiar contexts of, for example, Ferris wheels, merry-go-rounds, and bicycle wheels. These functions are fundamental to understanding many natural oscillatory phenomena, such as lunar illumination, tidal variation, and wave propagation.

Source – Subject Outline, South Australian Certificate of Education 2023

SACE Stage 1 Mathematics Courses

SACE Stage 1 Mathematics Syllabus

## Course Content

### Vectors

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Trigonometric Graphs
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Trigonometric Identities
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Reciprocal Trigonometric Functions
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• 35 Lessons
• 176 Topics
• 74 Quizzes