Achievement objective M7-4

 

Indicators

• 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 M7-7.

Progression

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 NZQA website.

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

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