# 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*.

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

**Fig. 546.** Natural logarithm ln *x*

**Fig. 547.** sin *x*

**Fig. 548.** cos *x*

**Fig. 549.** tan *x*

**Fig. 550.** cot *x*

**Tangent, cotangent, ...**