## Introduction: Trigonometric Functions

In electronics it is important that one be able to recognize wave patterns and their meanings. A good understanding of the trigonometric functions (SIN, COS, TAN, CSC, SEC, COT) is a must.

The following program will graph these functions and facilitate the study of AMPLITUDE, PHASE SHIFT, VERTICAL TRANSLATION and PERIOD. One is able to graph functions that are ADDED, SUBTRACTED, ABSOLUTE VALUE, and functions raised EXPONENTIALLY.

For the biginner, it is best to experiment using one function, the SIN for example. Procede as follows and use the (H)ELP screen frequently to check out definitions:

NOTE: If you succeed in mastering only the SIN and the COS functions you are doing well.

a) Do Amplitude, Period, Phase Shift, and Vertical Tanslation with SIN. Do several examples of each on the SIN function until you are comfortable with the meaning of each operation.

b) Repeat the above using the COS function.

c) Using only the SIN and the Cos functions, experiment doing ADDITION, SUBTRUATION, ABSOLUTE VALUE, and EXPONENTIALS.

d) Experiment using the other Trig functions. Look up the meaning of the word ASYMPTOTE and graph the TAN function. See the curve a-s-y-m-p-t-o-t-e !

When you RUN PT.EXE wait a few seconds while the program loads and auto-executes.

Ignore the address, etc., on the title page.

## 5 Comments

5 years ago

What OS does this program work on?

15 years ago

"In electronics it is important that one be able to recognize wave patterns and their meanings." Why?

Reply 15 years ago

Dear mikesty: I wish to correct an erro I made in my reply to your quiry dated Nov 18 2006 3:19 PM. In the second paragraph '117 Volts' should read '165 Volts', as follows: :::The wave patern of DC electricity is a straight line while the wave patern of a 110V house electrical supply is a (SIN) sinusoidal wave which changes direction 120 times per second: going from zero volts to +165 Volts(peek) and back to zero Volts; then down to -165 Volts (peek) and back to zero Volts in 1/60 seconds. What we call 117 Volts (commomly called 110 volts) is the RMS (root mean square) of the +165 peek voltage on the line. Use the TP.EXE program and set the (p or period) frequency to 60. Display the results and you will have a 'picture' of a house supply voltage::: NOTE :: The RMS voltage (not the peek) is used to calculate the EFFECTIVE POWER on the line. Sorry if I mislead you, Richard

Reply 15 years ago

Hi mikesty:

Since we cannot see electricity we rely on instruments to give us data we can interpret. Most multimeters will give us a snapshot or instantaneous reading of voltage, resistance and current. To understand what is going on in a cirsuit during a period of time (as opposed to instantaneously) we need to have a 'picture' of electrical variations or behaviour (voltsage, current, frequency, for example) taking place.

The wave patern of DC electricity is a straight line while the wave patern of a 110V house electrical supply is a (SIN) sinusoidal wave which changes direction 120 times per second: going from zero volts to +117 Volts(peek) and back to zero Volts; then down to -117 Volts (peek) and back to zero Volts in 1/60 seconds. What we call 110 or 117 Volts is the RMS (root mean square) of the +117 volt peek and the - 117 volt peek on the line. Use the TP.EXE program and set the (p or period) frequency to 60. Display the results and you will haave a 'picture' of a house supply voltage.

When two electrical (or sound) waves of different frequencies are mixed they add and subtract and produce a new and different wave with new chararteristics. This is called HETERODYNING in radio parlance. It can only be understood by wave annalysis.

Two strings (guitar,violin,piano) that are not vibrating at the same frequency will produce a BEAT frequency which is the ARITHMETIC difference of their induvidual frequencies.

Try this using TP.EXE: (C)lear the screen. secect "+" and enter F1 as SIN(x). Enter F2 as COS(x). Press ENTER to display the equation Y=SIN(X)+COS(X). Press ENTER. The display will show THREE waves; the SIN wave, the COS wave and the sum of these two waves, which is an entirely new wave with different characteristics. Where the waves add to form a PEEK you have a BEAT (the beat frequency).

A pure SIN wave of 440 cycles per second (called A440 or middle A on the piano keyboard) is the standard for tuning musical instruments so that they will play in harmony.

Pardon my long-winded reply.

Sincerely, Richard

15 years ago

An FFT can be used to express a sound as a "fourier series". Every sound is just a bunch of CONTINUOUS Sine waves added together. If you know which ones, you can synthesize ANY sound.