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Contents
Trigonometric Functions
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Trigonometric
Functions
The
definitions and manipulation of trigonometric functions can be found in our
section on trigonometry.
In
this section, we are concerned with graphs of trigonometric functions. We will
introduce the shape of the graphs, discuss the properties of the graphs as well
as demonstrate the transformation of their graphs.
Definitions
There
are some terms commonly used in the description of trigonometric functions.
Period
: The interval over which the graph of a function repeats itself.
Peak
: The maximum value of a function. In this section, it is applicable only
to the sine and cosine curves.
Trough
: The minimum value of a function. In this section, it is applicable only
to the sine and cosine curves.
Amplitude
: The largest deviation from the zero point which the curve can reach
Frequency
: The number of periods that occurs in 360o.
The
graphs here are in degrees, do note that it can be converted to radians.
Applications
The
sine and cosine curves appear in nature. Transverse waves follow this shape
(note that the sine and cosine curves are basically translations of each
other). The representation of sound waves on a cathode-ray oscilloscope also
follow this shape. Another common example is the graph of the voltage of the
alternating current output in a generator.
Tangent
and the reciprocal function graphs are rarely seen.
Most
of the graphs in this section are the drawings of our coach, Mr. Lim Poh
Kheng. Used with permission.
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