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4 Elementary FunctionsHyperbolic Functions

§4.29 Graphics


§4.29(i) Real Arguments

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Figure 4.29.1: sinhx and coshx. Magnify
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Figure 4.29.2: Principal values of arcsinhx and arccoshx. (arccoshx is complex when x<1.) Magnify
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Figure 4.29.3: tanhx and cothx. Magnify
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Figure 4.29.4: Principal values of arctanhx and arccothx. (arctanhx is complex when x<-1 or x>1, and arccothx is complex when -1<x<1.) Magnify
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Figure 4.29.5: cschx and sechx. Magnify
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Figure 4.29.6: Principal values of arccschx and arcsechx. (arcsechx is complex when x<0 and x>1.) Magnify

§4.29(ii) Complex Arguments

The conformal mapping w=sinhz is obtainable from Figure 4.15.7 by rotating both the w-plane and the z-plane through an angle 12π, compare (4.28.8).

The surfaces for the complex hyperbolic and inverse hyperbolic functions are similar to the surfaces depicted in §4.15(iii) for the trigonometric and inverse trigonometric functions. They can be visualized with the aid of equations (4.28.8)–(4.28.13).