Nayland College

Nayland College - Mathematics

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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

AS 2.4 Achievement Objectives

Triangles HOME | Achievement Criteria | Pythagoras | Trigonometry | Area | Sin Rule | Cosine Rule | Revision




  • Apply trigonometric relationships in solving problems.


  • Apply trigonometric relationships, using relational thinking, in solving problems.

  • Apply trigonometric relationships, using extended abstract thinking, in solving problems.

This involves:

- selecting and using methods

- demonstrating knowledge of trigonometric concepts and terms

- communicating using appropriate representations.

involves one or more of:

- selecting and carrying out a logical sequence of steps

- connecting different concepts or representations

- demonstrating understanding of concepts

- forming and using a model;

and also relating findings to a context, or communicating thinking using appropriate mathematical statements.

involves one or more of:

- devising a strategy to investigate or solve a problem

- identifying relevant concepts in context

- developing a chain of logical reasoning, or proof

- forming a generalisation;

and also using correct mathematical statements, or communicating mathematical insight.

Achievement Standard 3.10 #91582 (link to NZQA)

Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions


AS91259 Apply trigonometric relationships in solving problems

For the award of Achieved the requirements include selecting and using methods.
To be used as evidence, a ‘method’ must be relevant to the solution of the problem.
The ‘methods’ also need to be at the appropriate curriculum level for the standard.

At this level the trigonometric relationships for triangles involve non-right angled triangles.

The evidence from calculations involving any of the methods from EN4 must be in the context of solving a problem and so need to have a purpose (for example determining a total area that will be subdivided).

At all levels there is a requirement relating to the communication of the solutions.

At Achieved level, the result of a numerical calculation only is insufficient, working is expected and students need to indicate what the calculated answer represents.

At Merit level students need to clearly indicate what they are calculating and their solutions need to be linked to the context.

At Excellence level the response needs to be clearly communicated with correct mathematical statements and students need to explain any decisions they make in the solution of the problem.









Solve trigonometry problems requiring straightforward modelling of practical situations.


· sine rule

· cosine rule

· area of triangle

· sectors and segments

· circular measure, radians etc.

Situations to be modelled could involve:

· land measurement

· navigation.



Solve trigonometry problems requiring modelling of practical situations.

· Problems will be based on non-right-angled triangles where the choice of technique and the measurements are not easily identifiable, eg bearings



Solve multi-step trigonometry problems.

Problems could include:

· 2D representations of a 3D situation

· Use of more than one trigonometric formula

· Evaluation of the process and results of the practical task.

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