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
M8-6 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
, 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
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.
Note: Aligned and registered level 3 achievement standards will not be on the NZQA website until December 2012.
- School planning draft level 3 achievement standards are on
NCEA on TKI.
- Final draft level 3 achievement standards will be on
NCEA on TKI from end of September.
- Aligned level 3 achievement standards will be registered and published by NZQA for use in 2013 in December.
Full information on the level 3 draft standards and the alignment process can be found on
NCEA on TKI.
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 draft standards matrix.
Last updated September 26, 2012