Beyond SOHCAHTOA:
The Trigonometry Page
UNH Mathematics Center
Fall 2000
Hello, Calculus students! Our hope in these
pages is to free you from the SOHCAHTOA approach to
trigonometry.
You do remember SOHCAHTOA, don't you? It's an old mantra
for ''sine is opposite over hypotenuse, cosine is
adjacent over hypotenuse, tangent is opposite over adjacent.''
Lots of students are resigned to learning trigonometry in this way,
as a major memorization task.
But, that's not how the subject actually begins.
Although the trigonometric
functions eventually lead us to
unexpected and surprisingly useful results, trigonometry
begins with this question:
Suppose we have a length, or a vector. It's neither vertical
nor horizontal, but placed at an angle.
Can we resolve this angular distance into its vertical and
horizontal components?
You can see right away what the first questions are:
- How should we measure and
describe the
angle (or rotation)
of the ''slanted'' vector?
- We can see that when the angle is fixed, the
lengths of any angular vector's
vertical and horizontal components will be proportional to
the length of the angular vector.
(Sketching a few different angular vectors and
their vertical and horizontal components will show us the similar
triangles!) How should we describe these
proportionality constants?
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On 6 Dec 2000, 14:28.