# APPENDIX 3

# Auxiliary Material

## A3.1 Formulas for Special Functions

*For tables of numeric values, see Appendix 5.*

**Exponential function** *e** ^{x}* (Fig. 545)

**Natural logarithm** (Fig. 546)

ln *x* is the inverse of *e** ^{x}*, and

*e*

^{lnx}=

*x*,

*e*

^{−ln x}=

*e*

^{ln}(1/

*x*) = 1/

*x*.

**Logarithm of base ten** log_{10}*x* or simply log *x*

log *x* is the inverse of 10* ^{x}*, and 10

^{logx}=

*x*, 10

^{−log x}= 1/

*x*.

**Sine and cosine functions** (Figs. 547, 548). In calculus, angles are measured in radians, so that sin *x* and cos *x* have period 2π.

sin *x* is odd, sin (−*x*) = −sin *x*, and cos *x* is even, cos (−*x*) = cos *x*.

**Tangent, cotangent, ...**

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