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Trigonometry

Topic Overview

Trigonometry is one of the most important topics in Higher Level Leaving Cert maths. It is also one of the most problematic for many students. It is hard to avoid trigonometry, as well as accounting for two full questions out of seven in Section A of Paper 2, trigonometry is required in many other areas of the course, e.g., complex numbers, differentiation, integration and vectors.

Originally trigonometry was purely the study of triangles, but it has been expanded greatly since then. Our course reflects this development. We study triangles, sectors, circles, trigonometry ratios as well as the more general trigonometry functions. We learn how to prove trigonometry identities and how to solve trigonometry equations. We also examine inverse trigonometry functions and investigate a well-known trigonometry limit.

Topic Structure
 
The study of Senior Cycle Trigonometry can be divided into the following sections.

1. Fundamentals of Trigonometry
This relation can be used to convert between radians and degrees
Know exactly which ratio is which
These specail values can be found on page 9 of the Maths Tables
Using the unit circle definition
Make sure you know how to use your particular calculator

2. Trigonometry of the triangle and other figures
These can only be used for right angled triangles
Know how to determine which rule should be used
This is given on page 6 of the Maths Tables
These are given on pages 6 and 7 of the Maths Tables
Break the diagram into individual triangles, and note the connections between them

3. Trigonometric Identities
All the trig identities on page 9 of the Maths Tables can be used to prove other identities
The proofs of these may be examined
Obtained from the compound angle formulae by putting B=A
When using these, it is usual to put t=tanA
The proofs of these are not on the course

4. Trigonometric Equations
Leaving out solutions will cost you dearly in the exam
Write the equation in terms of one trig function, in this case cos

5. Inverse Trigonometric Functions and Limits
Practice drawing the graphs
This limit is mainly used in differentiation

Links
http://www.np.edu.sg/~bms/TrigFns/TrFn.htm
This excellent site contains many worked examples in each area, with questions given on each page. A number of questions are interactive, but to avail of this you have to first download the free MathView Internet plugin - it only takes a short while and is well worth having.

http://www.np.edu.sg/~bms/Add_Trig/addtrig.htm
More interactive notes from the same site covering additional topics in trigonometry.

http://aleph0.clarku.edu/~djoyce/java/trig/index.html
'Dave's Short Trig Course' offers a good basic introduction to this topic, although the pages at the end of the site are more likely to be of interest to higher level students. A number of the diagrams are interactive and can be manipulated or customised by the visitor.

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