Achievement objective M86
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.
Indicators
 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
M87, displaying and integrating graphs
M82, and gradient functions
M811.
 See
key mathematical ideas on NZmaths.
Progression
M86 links from M74, M76.
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 2d or 3d 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 subjectspecific 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
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