A Rational Approach to Trigonometry

Short Description
The trigonometry which you learnt at school is the wrong trigonometry. Young people over the. ages have been taught a theory which unnecessarily complicates …

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Content
A Rational Approach to Trigonometry
N J Wildberger
School of Maths UNSW Sydney
Australia 2052
January 24, 2007
The trigonometry which you learnt at school is the wrong trigonometry. Young people over the
ages have been taught a theory which unnecessarily complicates the subject and leads to loss of
accuracy in practical applications. Unfortunately continual repetition has cemented this approach
in the minds of educators as the only one possible-as you shall see, this is a mistake.
The thinking for the last two thousand years rests on the false assumptions that distance is the
best way of measuring the separation of points, and that angle is the best way of measuring the
separation of lines. So in order to study triangles students must first understand circles; they
learn about ?, lengths of circular arcs and the transcendental circular functions such as cos ? and
sin ? that relate arc length on a circle to x and y projections. They study the relations between
the circular functions and their inverse functions, ponder complicated graphs, and try to
remember lots of special values. Advanced students see the infinite power series that calculators
use to approximate true values. This is complicated stuff,…