It took some time

but I just came across the most marvelous short course in Trig that’s written in an engaging, fun and informative style! To wit:

… Hipparchus (190-120 B.C.E.) produced the first trigonometric table for use in astronomy. It was a table of chords for angles in a circle of large fixed radius. Incidentally, his table was not in terms of degrees, but “steps,” each step being 1/24 of a circle. Later, Ptolemy (100-178 C.E.) constructed a more complete table of chords. His table had chords for angles increasing from 1/2 degree to 180 degrees by steps of 1/2 degree. It also included aids for interpolating chords for minutes of angle. Ptolemy used a different large fixed radius than Hipparchus. The advantage of a large radius is that fractions can be avoided. In contrast, our present-day trigonometric functions are based on a unit circle, that is, a circle of radius 1. Of course using a unit circle doesn’t avoid fractions, but we have decimal fractions which are easy to work with.

Although trigonometry was, and still could be, based on chords as the primary trigonometric function, a slight modification of chords, called “sines,” turns out to be more convenient. Sines were first used in India a few centuries after chords were first used in ancient Greece. Sines are described on the next page ….MORE….

The whole course is comprehensive - your kids can learn about:

• Angle measurement
• Sines
• Cosines
• Tangents and slope
• The trigonometry of right triangles
• The trigonometric functions and their inverses
• Computing trigonometric functions
• The trigonometry of oblique triangles
• Demonstrations of the laws of sines and cosines

If your kids are learning trig now and having some trouble, this site is truly topnotch!

Hope the above resources are useful,

Owlbert

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ps - speaking about Trigonometry:

Trigonometry by Larson and Hosteler (2004)

Algebra and Trigonometry, Michael Sullivan, Very Good B

Algebra And Trigonometry With Analytic Geometry 11th ed

Algebra And Trigonometry (2006)

Fundamentals of Trigonometry. Swokowski. 8th edition

Trigonometry Demystified by Stan Gibilisco (2003)

trigonometry approach

SPEEDSTUDY TRIGONOMETRY Homeschool Learning Program

MATH, ALGEBRA, TRIGONOMETRY, CALCULUS CD (3127 pgs)

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