AS91575: Apply Trigonometric Methods in Solving Problems:

Course Overview

AS91575: Apply Trigonometric Methods in Solving Problems:

Internal Assessment Preparation

This course is designed specifically for NCEA Level 3 learners, with a strong focus on the

Trigonometry Internal Assessment. The content targets the core trigonometric skills,

reasoning, and methods that are most commonly required for success in Level 3 internal

assessments across schools.

The central objective of this course is to develop a clear, systematic approach to solving

trigonometric equations. Strong emphasis is placed on obtaining both general solutions and

specific solutions using algebraic methods, rather than relying on graphical or calculator-

based techniques. This level of algebraic control is essential not only for internal assessments,

but also for external assessments, particularly in differentiation, where trigonometric

equations frequently appear within larger problems.

A key emphasis of the course is on proof-style questions and structured trigonometric

reasoning. While some of these proof-type questions may not always appear directly in the

final internal assessment task, the thinking processes, algebraic techniques, and logical

structure developed through them are extremely valuable. This depth of understanding plays

a crucial role in handling internal tasks confidently and accurately.

The course systematically develops methods involving compound angle formulae, double-

angle formulae, and related identities. These techniques are essential not only for internal

assessments but also for handling Excellence-level reasoning in differentiation, integration,

and complex algebra, where trigonometric manipulation often becomes a decisive factor.

Although the course is compact, typically requiring an investment of around 12–14 focused

hours, it is designed to deliver high impact. Consistent engagement with the methods taught

here significantly improves confidence in solving trigonometric equations and reduces

common errors that occur when trigonometry appears at the final stages of longer problems.

Many learners manage calculus techniques such as differentiation, optimisation, and

integration well, but lose Excellence due to weak trigonometric handling at the conclusion

of a solution. This course directly addresses that gap by strengthening method selection,

algebraic accuracy, and final reasoning.

It is important to note that internal assessments can vary between schools, and some schools

may allow the use of graphing software for solving trigonometric equations. (This course

does not cover Graphical method for solving trigonometric equations). However, the

algebraic understanding developed in this course remains essential, particularly for

external assessments, where such tools are not permitted. The skills developed here

therefore provide long-term value beyond a single assessment.

Overall, this course plays a critical role in building the depth, control, and confidence

required for high-quality trigonometric reasoning, supporting strong performance in internal

assessments and strengthening readiness for Merit and Excellence-level external

examinations.