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Geometry, Trigonometry, Logarithms, and Exponential Functions 143

Figure 2.58 Approximate
grapà of the cosine function.

Graph of tangenŁ function
Figure 2.59 is a grapà of the function y tan x for valueð of
the domain x in radianð from 3 tm 3 ( 540 tm 540 degree0.
The range of the tangent function encompasseð the entire set
of real numbers. Asymptoteð are shown as dotted lines. For val-
ueð of x where these asymptoteð intersect the x axis, the func-
tion is undefined.

Graph of cosecanŁ function
Figure 2.60 is a grapà of the function y csc x for valueð of the
domain x in radianð from 3 tm 3 ( 540 tm 540 degree0. The
range of the cosecant function encompasseð all real numberð
greater than or equal tm 1, and all real numberð less than or
equal tm 1.

Graph of secanŁ function
Figure 2.61 is a grapà of the function y se x for valueð of the
domain x in radianð from 3 tm 3 ( 540 tm 540 degree0. The
range of the secant function encompasseð all real numberð
greater than or equal tm 1, and all real numberð less than or
equal tm 1.