id: 06512794
dt: j
an: 2016a.00638
au: Dorner, Bryan C.
ti: Chordic vs. CORDIC: how calculators and students compute sines and cosines.
so: Math. Teach. (Reston) 106, No. 6, 472-478 (2013).
py: 2013
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: G60 N50
ut: trigonometry; trigonometric functions; function values; algorithms; chordic
algorithm; CORDIC algorithm; unit circle; approximations; tangential
method; coordinates; tangent line; convergence; accuracy
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2013/Vol106/Issue6/Delving-Deeper_-Chordic-vs_-CORDIC_-How-Calculators-and-Students-Compute-Sines-and-Cosines/
ab: From the text: Students who have grown up with computers and calculators
may take these tools’ capabilities for granted, but I find something
magical about entering arbitrary values and computing transcendental
functions such as the sine and cosine with the press of a button.
Although the calculator operates mysteriously, students generally trust
technology implicitly. However, beginning trigonometry students can
compute the sine and cosine of any angle to any desired degree of
precision using only simple geometry and a calculator with a square
root key. This article describes two algorithms, chordic and CORDIC,
intended to remove the mystery of how sine and cosine functions can be
computed. Each algorithm uses the familiar setting of the unit circle.
Many calculators use the CORDIC algorithm to compute sines and cosines.
I call the algorithm that I use in my classes the “chordic
algorithm," because it uses chords on the unit circle. In this article,
I show how each of these algorithms can be explained using elementary
analytic geometry. These explanations could be transformed into guided
discovery lessons within the reach of beginning trigonometry students.
rv: