Achievement objective M7-4
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:
- apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions.
- Solves problems that can be modelled by trigonometric relationships.
- Proves simple trigonometric identities making links to right-angled triangles.
- Uses the area formula for triangles and the sine and cosine rules to solve problems.
- Uses knowledge of right-angled triangles to find exact values of the trig ratios.
- Uses radian measure.
- Makes links between the unit circle
M7-1, graphs of trig functions
M7-2, and solutions of trig equations
M7-4 links from GM6-5, GM6-6 and to M8-6, M8-7.
What is new/changed?
- This was previously located in the geometry strand at level 6.
Possible context elaborations
- Sample identities include: sin2x + cos2x = 1,
Sample exact values could include:
- Arc length and area of sector problems:
- semi-circular cross section trough problems
- security light coverage using sectors
- radar overlapping areas, search and rescue situations
- alternating voltage applications from physics using unit circle.
Height measurement: Finding the height of an object
How far is it: Cosine rule
Navigation problem: Cosine rule
Sand: Finding the natural angle of inclines.
Sine rule introduction
Spherical shapes: Finding the angle between two points and the centre on a variety of balls.
- Water sprinklers: Some water sprinklers continually turn left and right to water an area of lawn. The water lands on the ground a distance from the sprinkler. Work out the area of grass being watered.
- Petrol barrel: A petrol barrel is lying on its side. How much petrol is left in the barrel? Draw a barrel end and include on it a volume scale.
- Rotary clothesline: A rotary clothesline can have many shapes. Square, rectangle, pentagon or even hexagon. How much wire is needed for any one of these if they have 3 wires, 4 wires etc.
- Use the length of your shadow to work out your height.
- Calculate the angles on your bicycle frame.
- Bolts: work out the distance that a bolt moves in a full turn. Compare several bolts. Compare the jack of a small car with the jack of a larger/older car. How does the thread differ?
- A sharp pencil or pen has a tapered point. Measure distances to find the angle of the taper. Compare this with the taper of pencil sharpeners.
- Work out the angle of a roof. Use this to find the height of the top of a roof.
Assessment for qualifications
NCEA achievement standards at level 1 and 2 have been aligned to the New Zealand Curriculum. Please ensure that you are using the correct version of the standards by going to the
Aligned level 3 achievement standards will be registered by NZQA for use in 2013.
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.
- AS91259 Mathematics and statistics 2.4 Apply trigonometric relationships in solving problems
Refer to the draft standards matrix.
Last updated September 26, 2012