*Date of the lesson: 31 Oct 2011*

In order to solve exercises involving vectors, trigonometric identities come very handy. For instance:

And don’t forget the prosthaphaeresis formulae!

One important relationship is the Law of Sines:

Summing vector is easy as long as you project each vector along the coordinate axes. Five steps north, two steps east, three steps south…

How to fly a plane from Bologna to Prague:

http://www.algebralab.org/Word/Word.aspx?file=Trigonometry_ResultantsDotProducts.xml

Wanna try to land your cessna airplane? Click this link for a nice flash game. Why don’t you code an android applet for you mobile phone instead?

### Exercises

- Calculate and , where: ,
- The resultant vector has length . The angle between and is . Knowing that the angle , find the length of and .
- Calculate the angle between ,
- For the die-hard: calculate the area of the triangle defined by vertices A(-1,2,3) B(2,-1,1) C(1,3,2)

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I didn’t find the last one really difficult… with Sarros it was fast!

Anyway we’ll go through them tomorrow. See you!

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