# My Trig Book

#### Abstract

This is the MATH 117 Trigonometry text developed by Dr. Bruce Kessler for the Gatton Academy of Math and Science at Western Kentucky University for the Academy sections of the course. The text has also been used in two online course offerings. Revised 7/19/11.

Free readers are available for all of the files that accompany the book. Mathematica Player is available at http://www.wolfram.com/products/player/. QuickTime Player is available at http://www.apple.com/quicktime/.

#### Suggested Citation

Bruce Kessler. My Trig Book. , 2010. Available at: http://works.bepress.com/bruce_kessler/1

*This Mathematica file simulates a projectile launcher, and allows the student to conduct their own experiment to find the velocity of the launcher. (Chapter 2)*

Virtual_Tar-getter.nb (113 kB)

*This Mathematica file simulates a projectile launcher, and allows the student to see if their firing angles will hit the target. (Chapter 2)*

spirograph.mov (1439 kB)

*This is a QuickTime movie of a Spirograph curve being drawn. (Chapter 3)*

spirograph.nb (14 kB)

*This Mathematica file allows students to simulate using a Spirograph to draw their own curves. (Chapter 3)*

orbitalmotion.nb (17 kB)

*This Mathematica file allows students to draw their own curves depicting orbital motion. (Chapter 3)*

unitcircle.nb (470 kB)

*This is a Mathematica file showing how the x- and y- coordinates on the unit circle corresponding to different whole number angles (Chapter 4).*

unitcircle.mov (597 kB)

*This is a QuickTime movie showing how the x- and y- coordinates on the unit circle corresponding to different whole number angles (Chapter 4).*

sine.nb (6486 kB)

*This is a Mathematica file showing how the graph of the sine function is generated from the y- coordinates as a point is rotated about the unit circle (Chapter 4).*

sine.mov (301 kB)

*This is a QuickTime movie showing how the graph of the sine function is generated from the y- coordinates as a point is rotated about the unit circle (Chapter 4).*

cosine.nb (6370 kB)

*This is a Mathematica file showing how the graph of the cosine function is generated from the x- coordinates as a point is rotated about the unit circle (Chapter 4).*

cosine.mov (306 kB)

*This is a QuickTime movie showing how the graph of the cosine function is generated from the x- coordinates as a point is rotated about the unit circle (Chapter 4).*

tan1.nb (7070 kB)

*This is a Mathematica file showing how the graph of the tangent function is generated from the slope of the ray and a point being rotated about the unit circle (Chapter 4).*

tan1.mov (396 kB)

*This is a QuickTime movie showing how the graph of the tangent function is generated from the slope of the ray and a point being rotated about the unit circle (Chapter 4).*

sinecosine.nb (17508 kB)

*This is a Mathematica file showing graphically the product of the sine and cosine functions and how that relates to the double-angle identity for sine (Chapter 4).*

sinecosine.mov (341 kB)

*This is a QuickTime movie showing graphically the product of the sine and cosine functions and how that relates to the double-angle identity for sine (Chapter 4).*

squaresdiff.nb (34261 kB)

*This is a Mathematica file showing graphically the difference between the squares of the cosine function and the sine function, and how it relates to the double-angle identity for cosine (Chapter 4).*

squaresdiff.mov (457 kB)

*This is a QuickTime movie showing graphically the difference between the squares of the cosine function and the sine function, and how it relates to the double-angle identity for cosine (Chapter 4).*

tan2.nb (14935 kB)

*This is a Mathematica file showing how the graph of the tangent function is generated as the quotient of the sine and cosine functions (Chapter 4).*

tan2.mov (500 kB)

*This is a QuickTime movie showing how the graph of the tangent function is generated as the quotient of the sine and cosine functions (Chapter 4).*

cot.nb (14840 kB)

*This is a Mathematica file showing how the graph of the cotangent can be generated as the quotient of the cosine and sine functions (Chapter 4).*

cot.mov (495 kB)

*This is a QuickTime movie showing how the graph of the cotangent can be generated as the quotient of the cosine and sine functions (Chapter 4).*

sec.nb (15072 kB)

*This is a Mathematica file showing how the graph of the secant function can be generated as the multiplicative inverse of the cosine function (Chapter 4).*

sec.mov (382 kB)

*This is a QuickTime movie showing how the graph of the secant function can be generated as the multiplicative inverse of the cosine function (Chapter 4).*

csc.nb (15653 kB)

*This is a Mathematica file showing how the graph of the secant function can be generated as the multiplicative inverse of the sine function (Chapter 4).*

csc.mov (389 kB)

*This is a QuickTime movie showing how the graph of the secant function can be generated as the multiplicative inverse of the sine function (Chapter 4).*

basesandslope.mov (1403 kB)

*This is a QuickTime movie showing how the slope of a tangent line at (0,1) to an exponential function changes with the base (Chapter 5).*

expapprox.mov (1070 kB)

*This is a QuickTime movie showing the convergence of the exponential function to its infinite polynomial (power series) representation (Chapter 5).*

sinapprox.mov (799 kB)

*This is a QuickTime movie showing the convergence of the sine function to its infinite polynomial (power series) representation (Chapter 5).*

cosapprox.mov (805 kB)

*This is a QuickTime movie showing the convergence of the cosine function to its infinite polynomial (power series) representation (Chapter 5).*

thirdrootsunity.mov (483 kB)

*This is a QuickTime movie showing how each of the third roots of unity go to 1 when cubed (Chapter 5).*

CORDIC.nb (41 kB)

*This is a Mathematica file that utilizes the CORDIC algorithm (Chapter 5).*

transversal1.mov (76 kB)

*This is a QuickTime movie showing a transversal wave (Chapter 6).*

transversal2.mov (188 kB)

*This is a QuickTime movie showing a transversal wave (Chapter 6).*

longitudinal.mov (53 kB)

*This is a QuickTime movie showing a longitudinal wave (Chapter 6).*

together.mov (142 kB)

*This is a QuickTime movie showing how a longitudinal wave is equivalent to a transversal wave (Chapter 6).*

Fourierseries.mov (243 kB)

*This is a QuickTime movie showing the convergence of a Fourier series to a particular discontinuous function (Chapter 6).*

dchord.wav (86 kB)

*This is a WAVE file (playable with QuickTime) of a D-chord played on a synthesizer (Chapter 6).*

frequencies.nb (538 kB)

*This is a Mathematica file that helps spot frequencies in digital sound files (Chapter 6).*

dchord_guitar.wav (86 kB)

*This is a WAVE file (playable with QuickTime) of a D-chord played on a guitar (Chapter 6).*

dchord_twosec.wav (172 kB)

*This is a WAVE file (playable with QuickTime) of a D-chord played on a synthesizer for two seconds (Chapter 6).*

noise.wav (180 kB)

*This is a WAVE file (playable with QuickTime) of a noisy lobby of people (Chapter 6).*

ex1.wav (172 kB)

ex2.wav (818 kB)

ex3.wav (172 kB)

ex4.wav (258 kB)

ex5.wav (430 kB)

ex6.wav (947 kB)

ex7.wav (861 kB)

ex8.wav (86 kB)

ex9.wav (516 kB)

ex10.wav (258 kB)

lalala.wav (211 kB)

*This is a WAVE file (playable with QuickTime) of someone signing (Chapter 6).*

lowerfrequency.nb (25 kB)

*This Mathematica file enables the user to lower the frequency of a voice by one octave (Chapter 6).*

lowlalala.wav (210 kB)

*This is a WAVE file (playable with QuickTime) showing the effect of lowerfrequency.nb on lalala.wav (Chapter 6).*

ex11.wav (344 kB)

filtering.nb (13 kB)

*This Mathematica file enables the user to filter out certain frequencies from a digital sound file (Chapter 6).*

singing.wav (445 kB)

*This is a WAVE file (playable with QuickTime) of someone singing (Chapter 6).*

singing_static.wav (447 kB)

*This is a WAVE file (playable with QuickTime) of someone singing with static introduced (Chapter 6).*

singing_whistle.wav (499 kB)

*This is a WAVE file (playable with QuickTime) of someone singing with a whistle introduced (Chapter 6).*

ex12.wav (172 kB)

ex13.wav (818 kB)

ex14.wav (430 kB)

ex15.wav (947 kB)

ex16.wav (839 kB)

ex17.wav (836 kB)

ex18.wav (862 kB)

ex19.wav (1293 kB)

ex20.wav (561 kB)

ex21.wav (518 kB)

ex22.wav (23 kB)

ex23.wav (172 kB)

ex24.wav (561 kB)

ex25.wav (518 kB)