Tree-gonometry!

So here you are, at the end of your studies of Trigonometry. Take some time to think of all the new things you have learned – you have all covered so much, and you should be proud of what you have achieved.

Now it is time to get the reward your efforts have earned – this week is test week (both ODT & Trigonometry!). You know what skills we have practiced through our tests this year, and you need to be prepared for the same structure again – but you should be planning how you will best make use of your time, to demonstrate your knowledge. Remember what we have spoken about regarding “owning your test” – it belongs to you, and at the end it shows what you can do. Since it is all about you, it is yours to do with what you want to. Choose your own path!

Some of the things you have learnt are how trigonometry can be applied to non-perpendicular triangles (the sine & cosine rules).

These rules can be used with right-angled triangles as well, but are probably more difficult to use! Some of you are finding the Ambiguous case of the sine rule difficult to get your heads around, so here is a video that may help you understand:

There is another good video here – watch them both until you are sure you know how to handle these problems.

The next major skill you have to master is the trigonometry of navigation – bearings and vector resolution, and the relationship between global navigation and spherical trigonometry. I have found four videos that illustrate these ideas (1, 2, 3, 4).

You will also want to master the unit circle – ensure that you know how Sine, Cosine & Tangent all relate to parts of the Unit Circle, and identify which are positive in which quadrant.

There is a previous post on CyberChalky that goes into much greater detail – you may want to check it out.

Finally, the project that you are all working on – to use trigonometry to determine the height of an object (be it a tree, light tower or goal post). Your task was to use at least two different techniques (such as direct calculation, known distance, similar triangles, the “scout” tricks and technological tricks such as Iphone apps) to accurately find that height. There are three parts of the assessment:

1. The mathematical aspect: this includes explaining how the technique is applied, and the correct mathematical workings.
2. The accuracy aspect: taking into account the uncertainty in the physical measurement and calculating an appropriate range for answers
3. Reconciliation aspect: combining your answers from the different techniques in a meaningful way to justify a reasonable final answer.

You are expected to present your work as a coherent and well organised whole – this project assesses you ability to work mathematically as well as deal with real world measurements.

The final due date for this task is the 15th of August. A rubric will be posted here shortly.

See you in class!

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