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Achievement objective M8-6

In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:

  • manipulate trigonometric expressions.


  • Solves problems that involve manipulating trig expressions using a variety of trig identities, including:
    • the Pythagorean identities
    • compound angle formula
    • double angle formula
    • sums and products
    • reciprocal trigonometric functions.
  • Identifies and uses appropriate key features of trigonometric functions, that is, amplitude, period and frequency.
  • Makes links with solving equations M8-7, displaying and integrating graphs M8-2, and gradient functions M8-11.
  • See key mathematical ideas on NZmaths.


M8-6 links from M7-4, M7-6.

Possible context elaborations

  • Proving identities, for example, double angle, half angle, triple angle formulae.
  • Finding exact values of trig expressions, e.g. sin 105° and special triangles.
  • Examples include: Given Sin alpha equals three fifths. , Cos beta equals twelve thirteenths. , find the exact value of sin(α + β).
  • Using trigonometry to solve problems involving triangles in 2-d or 3-d situations.
  • Using the relationship between degree and radian measure to apply appropriate trig models to a given context.
  • Solving trigonometric equations, giving general solutions or solutions within a given domain.
  • Modelling situations such as tides using trigonometric functions.
  • Activity: Big Bang Theory - Exact values

Assessment for qualifications

NCEA achievement standards at levels 1, 2 and 3 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the NZQA website.

The NZQA subject-specific resources pages are very helpful. From there, you can find all the achievement standards and links to assessment resources, both internal and external.

Learn more:

The following achievement standard(s) could assess learning outcomes from this AO:

  • AS91575 Mathematics and statistics 3.3 Apply trigonometric methods in solving problems; Internal, 4 credits.

Refer to the mathematics and statistics matrix.

Last updated September 26, 2013