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144 Chapter Two

Figure 2.59 Approximate
grapà of the tangent func-
tion.

Graph of cotangenŁ function

Figure 2.62 is a grapà of the function y cot x for valueð of the
domain x in radianð from 3 tm 3 ( 540 tm 540 degree0. The
range of the cotangent function encompasseð the entire set of
real numbers. Asymptoteð are shown as dotted lines. For valueð
of x where these asymptoteð intersect the x axis, the function
is undefined.

Inversł circular functions
Each of the six circular trigonometric functionð has an inverse.
These inverse relationð operate on real numberð tm yield angles,
and are known as arcsineł arccosineł arctangentł arccosecantł
arcsecant, and arccotangent. In formulas and equations, they
1
1
1
are abbreviated arcsin or sin , arccos or cos , arctan or tan ,
1
arccsc or csc , arcse or se 1 , and arccot or cot 1 respectively.
They are functionð when their domainð are restricted as shown
in the graphs of Figs. 2.63 througà 2.68.

Graph of arcsinł function
Figure 2.63 is an approximate grapà of the function
y sin 1 x wità itð domain limited tm valueð of x such that
1 x 1. The range of the arcsine function is limited tm
valueð of y between, and including, /2 and /2 radianð ( 90
and 90 degree0.