Section: 17 | Constants |

How to Cite this Reference

1 CONSTANTS

$\begin{matrix} π & = & 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37511 \\ 1 / π & = & 0.31830 98861 83790 67153 77675 26745 02872 40689 19291 48091 \\ e & = & 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69996 \\ 1 / e & = & 0.36787 94411 71442 32159 55237 70161 46086 74458 11131 03177 \\ i^{i} & = & e^{- π / 2} = 0.20787 95763 50761 90854 69556 \\ \sqrt{2} & = & 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37695 \\ Euler"s Constant γ & = & 0.57721 56649 01532 86061 \\ Golden Ratio φ & = & 1.61803 39887 49894 84820 45868 34365 63811 77203 09180 \end{matrix}$

1.1 DECIMAL EQUIVALENTS OF FRACTIONS (INCHES TO MM)

$\frac{1}{16} inches$	$0.0625 inches$	$1.59 nm$
$\frac{1}{8} inches$	$0.125 inches$	$3.18 nm$
$\frac{3}{16} inches$	$0.1875 inches$	$4.76 nm$
$\frac{1}{4} inches$	$0.25 inches$	$6.35 nm$
$\frac{5}{16} inches$	$0.3125 inches$	$7.94 nm$
$\frac{3}{8} inches$	$0.375 inches$	$9.53 nm$
$\frac{7}{16} inches$	$0.4375 inches$	$11.1 nm$
$\frac{1}{2} inches$	$0.5 inches$	$12.7 nm$
$\frac{9}{16} inches$	$0.5625 inches$	$14.3 nm$
$\frac{5}{8} inches$	$0.625 inches$	$15.9 nm$
$\frac{11}{16} inches$	$0.6875 inches$	$17.5 nm$
$\frac{3}{4} inches$	$0.75 inches$	$19.1 nm$
$\frac{13}{16} inches$	$0.8125 inches$	$20.6 nm$
$\frac{7}{8} inches$	$0.875 inches$	$22.2 nm$
$\frac{15}{16} inches$	$0.9375 inches$	$23.8 nm$
$1 inches$	$1 inches$	$25.4 nm$

1.2 EXPONENTIAL AND HYPERBOLIC FUNCTIONS AND THEIR COMMON LOGARITHMS

	$\underset{̲}{e^{x}}$		$e^{- x}$	$\underset{̲}{sinh x}$		$\underset{̲}{cosh x}$
$x$	Value	${log}_{10}$	Value	Value	${log}_{10}$	Value	${log}_{10}$	tanh x Value
0.00	1.0000	0.00000	1.00000	0.0000	$- \infty$	1.0000	0.00000	0.00000
0.05	1.0513	.02171	.95123	.0500	$- 2.69915$	1.0013	.00054	.04996
0.10	1.1052	.04343	.90484	.1002	$- 1.00072$	1.0050	.00217	.09967
0.15	1.1618	.06514	.86071	.1506	$- 1.17772$	1.0113	.00487	.14889
0.20	1.2214	.08686	.81873	.2013	$- 1.30392$	1.0201	.00863	.19738
0.25	1.2840	.10857	.77880	.2526	$- 1.40245$	1.0314	.01343	.24492
0.30	1.3499	.13029	.74082	.3045	$- 1.48362$	1.0453	.01926	.29131
0.35	1.4191	.15200	.70469	.3572	$- 1.55290$	1.0619	.02607	.33638
0.40	1.4918	.17372	.67032	.4108	$- 1.61358$	1.0811	.03385	.37995
0.45	1.5683	.19543	.63763	.4653	$- 1.66777$	1.1030	.04256	.42190
0.50	1.6487	.21715	.60653	.5211	$- 1.71692$	1.1276	.05217	.46212
0.55	1.7333	.23886	.57695	.5782	$- 1.76204$	1.1551	.06262	.50052
0.60	1.8221	.26058	.54881	.6367	$- 1.80390$	1.1855	.07389	.53705
0.65	1.9155	.28229	.52205	.6967	$- 1.84308$	1.2188	.08593	.57167
0.70	2.0138	.30401	.49659	.7586	$- 1.88000$	1.2552	.09870	.60437
0.75	2.1170	.32572	.47237	.8223	$- 1.91504$	1.2947	.11216	.63515
0.80	2.2255	.34744	.44933	.8881	$- 1.94846$	1.3374	.12627	.66404
0.85	2.3396	.36915	.42741	.9561	$- 1.98051$	1.3835	.14099	.69107
0.90	2.4596	.39087	.40657	1.0265	.01137	1.4331	.15627	.21630
0.95	2.5857	.41258	.38674	1.0995	.04119	1.4862	.17208	.73978
1.00	2.7183	.43429	.36788	1.1752	.07011	1.5431	.18839	.76159
1.10	3.0042	.47772	.33287	1.3356	.12569	1.6685	.22233	.80050
1.20	3.3201	.52115	.30119	1.5095	.17882	1.8107	.25784	.83365
1.30	3.6693	.56458	.27253	1.6984	.23004	1.9709	.29467	.86172
1.40	4.0552	.60801	.24660	1.9043	.27974	2.1509	.33262	.88535
1.50	4.4817	.65144	.22313	2.1293	.32823	2.3524	.37151	.90515
1.60	4.9530	.69487	.20190	2.3756	.37577	2.5775	.41119	.92167
1.70	5.4739	.73830	.18268	2.6456	.42253	2.8283	.45153	.93541
1.80	6.0496	.78173	.16530	2.9422	.46867	3.1075	.49241	.94681
1.90	6.6859	.82516	.14957	3.2682	.51430	3.4177	.53374	.95624
2.00	7.3891	.86859	.13534	3.6269	.55953	3.7622	.57544	.96403
2.50	12.182	1.08574	.08208	6.0502	.78177	6.1323	.78762	.98661
3.00	20.086	1.30288	.04979	10.018	1.00078	10.068	1.00293	0.99505
3.50	33.115	1.52003	.03020	16.543	1.21860	16.573	1.21940	0.99818
4.00	54.598	1.73718	.01832	27.290	1.43600	27.308	1.43629	0.99933
4.50	90.017	1.95433	.01111	45.003	1.65324	45.014	1.65335	0.99975
5.00	148.41	2.17147	.00674	74.203	1.87042	74.210	1.87046	0.99991
5.50	244.69	2.38862	.00409	122.34	2.08758	122.35	2.08760	0.99997
6.00	403.43	2.60577	.00248	201.71	2.30473	201.72	2.30474	0.99999
6.50	665.14	2.82291	.00150	332.57	2.52188	332.57	2.52189	1.00000
7.00	1096.6	3.04006	.00091	548.32	2.73904	548.32	2.73903	1.00000
7.50	1808.0	3.25721	.00055	904.02	2.95618	904.02	2.95618	1.00000
8.00	2981.0	3.47436	.00034	1490.5	3.17333	1490.5	3.17333	1.00000
8.50	4914.8	3.69150	.00020	2457.4	3.39047	2457.4	3.39047	1.00000
9.00	8103.1	3.90865	.00012	4051.5	3.60762	4051.5	3.60762	1.00000
9.50	13360.	4.12580	.00007	6679.9	3.82477	6679.9	3.82477	1.00000
10.00	22026.	4.34294	.00005	11013.	4.04191	11013.	4.04191	1.00000

1.3 TRIGONOMETRIC FUNCTIONS TO FOUR DECIMAL PLACES

x radians	x degrees	$sin x$	$cos x$	$tan x$	$cot x$	$sec x$	$csc x$
.0000	$0^{\circ} 00^{'}$	.000	1.0000	.0000	–	1.000	–	$90^{\circ} 00^{'}$	1.5708
.0029	10	.0029	1.0000	.0029	343.8	1.000	343.8	50	1.5679
.0058	20	.0058	1.0000	.0058	171.9	1.000	171.9	40	1.5650
.0087	30	.0087	1.0000	.0087	114.6	1.000	114.6	30	1.5621
.0116	40	.0116	.9999	.0116	85.94	1.000	85.95	20	1.5592
.0145	50	.0145	.9999	.0145	68.75	1.000	68.76	10	1.5563
.0175	$1^{\circ} 00^{'}$	.0175	.9998	.0175	57.29	1.000	57.30	$89^{\circ} 00^{'}$	1.5533
.0349	$2^{\circ} 00^{'}$	.0349	.9994	.0349	28.64	1.001	28.65	$88^{\circ} 00^{'}$	1.5359
.0524	$3^{\circ} 00^{'}$	.0523	.9986	.0524	19.08	1.001	19.11	$87^{\circ} 00^{'}$	1.5184
.0698	$4^{\circ} 00^{'}$	.0698	.9976	.0699	14.30	1.002	14.34	$86^{\circ} 00^{'}$	1.5010
.0873	$5^{\circ} 00^{'}$	.0872	.9962	.0875	11.43	1.004	11.47	$85^{\circ} 00^{'}$	1.4835
.1047	$6^{\circ} 00^{'}$	.1045	.9945	.1051	9.514	1.006	9.597	$84^{\circ} 00^{'}$	1.4661
.1222	$7^{\circ} 00^{'}$	.1219	.9925	.1228	8.144	1.008	8.206	$83^{\circ} 00^{'}$	1.4486
.1396	$8^{\circ} 00^{'}$	.1392	.9903	.1405	7.115	1.010	7.185	$82^{\circ} 00^{'}$	1.4312
.1571	$9^{\circ} 00^{'}$	.1564	.9877	.1584	6.314	1.012	6.392	$81^{\circ} 00^{'}$	1.4137
.1745	$10^{\circ} 00^{'}$	.1736	.9848	.1763	5.671	1.015	5.759	$80^{\circ} 00^{'}$	1.3963
.1920	$11^{\circ} 00^{'}$	.1908	.9816	.1944	5.145	1.019	5.241	$79^{\circ} 00^{'}$	1.3788
.2094	$12^{\circ} 00^{'}$	.2079	.9781	.2126	4.705	1.022	4.810	$78^{\circ} 00^{'}$	1.3614
.2269	$13^{\circ} 00^{'}$	.2250	.9744	.2309	4.331	1.026	4.445	$77^{\circ} 00^{'}$	1.3439
.2443	$14^{\circ} 00^{'}$	.2419	.9703	.2493	4.011	1.031	4.134	$76^{\circ} 00^{'}$	1.3265
.2618	$15^{\circ} 00^{'}$	.2588	.9659	.2679	3.732	1.035	3.864	$75^{\circ} 00^{'}$	1.3090
.2793	$16^{\circ} 00^{'}$	.2756	.9613	.2867	3.487	1.040	3.628	$74^{\circ} 00^{'}$	1.2915
.2967	$17^{\circ} 00^{'}$	.2924	.9563	.3057	3.271	1.046	3.420	$73^{\circ} 00^{'}$	1.2741
.3142	$18^{\circ} 00^{'}$	.3090	.9511	.3249	3.078	1.051	3.236	$72^{\circ} 00^{'}$	1.2566
.3316	$19^{\circ} 00^{'}$	.3256	.9455	.3443	2.904	1.058	3.072	$71^{\circ} 00^{'}$	1.2392
.3491	$20^{\circ} 00^{'}$	.3420	.9397	.3640	2.747	1.064	2.924	$70^{\circ} 00^{'}$	1.2217
.3665	$21^{\circ} 00^{'}$	.3584	.9336	.3839	2.605	1.071	2.790	$69^{\circ} 00^{'}$	1.2043
.3840	$22^{\circ} 00^{'}$	.3746	.9272	.4040	2.475	1.079	2.669	$68^{\circ} 00^{'}$	1.1868
.4014	$23^{\circ} 00^{'}$	.3907	.9205	.4245	2.356	1.086	2.559	$67^{\circ} 00^{'}$	1.1694
.4189	$24^{\circ} 00^{'}$	.4067	.9135	.4452	2.246	1.095	2.459	$66^{\circ} 00^{'}$	1.1519
.4363	$25^{\circ} 00^{'}$	.4226	.9063	.4663	2.145	1.103	2.366	$65^{\circ} 00^{'}$	1.1345
.4538	$26^{\circ} 00^{'}$	.4384	.8988	.4877	2.050	1.113	2.281	$64^{\circ} 00^{'}$	1.1170
.4712	$27^{\circ} 00^{'}$	.4540	.8910	.5095	1.963	1.122	2.203	$63^{\circ} 00^{'}$	1.0996
.4887	$28^{\circ} 00^{'}$	.4695	.8829	.5317	1.881	1.133	2.130	$62^{\circ} 00^{'}$	1.0821
.5061	$29^{\circ} 00^{'}$	.4848	.8746	.5543	1.804	1.143	2.063	$61^{\circ} 00^{'}$	1.0647
.5236	$30^{\circ} 00^{'}$	.5000	.8660	.5774	1.732	1.155	2.000	$60^{\circ} 00^{'}$	1.0472
.5411	$31^{\circ} 00^{'}$	.5150	.8572	.6009	1.664	1.167	1.942	$59^{\circ} 00^{'}$	1.0297
.5585	$32^{\circ} 00^{'}$	.5299	.8480	.6249	1.600	1.179	1.887	$58^{\circ} 00^{'}$	1.0123
.5760	$33^{\circ} 00^{'}$	.5446	.8397	.6494	1.540	1.192	1.836	$57^{\circ} 00^{'}$	.9948
.5934	$34^{\circ} 00^{'}$	.5592	.8290	.6745	1.483	1.206	1.788	$56^{\circ} 00^{'}$	.9774
.6109	$35^{\circ} 00^{'}$	.5736	.8192	.7002	1.428	1.221	1.743	$55^{\circ} 00^{'}$	.9599
.6283	$36^{\circ} 00^{'}$	.5878	.8090	.7265	1.376	1.236	1.701	$54^{\circ} 00^{'}$	.9425
.6458	$37^{\circ} 00^{'}$	.6018	.7986	.7536	1.327	1.252	1.662	$53^{\circ} 00^{'}$	.9250
.6632	$38^{\circ} 00^{'}$	.6157	.7880	.7813	1.280	1.269	1.624	$52^{\circ} 00^{'}$	.9076
.6807	$39^{\circ} 00^{'}$	.6293	.7771	.8098	1.235	1.287	1.589	$51^{\circ} 00^{'}$	.8901
.6981	$40^{\circ} 00^{'}$	.6428	.7660	.8391	1.192	1.305	1.556	$50^{\circ} 00^{'}$	.8727
.7156	$41^{\circ} 00^{'}$	.6561	.7547	.8693	1.150	1.325	1.524	$49^{\circ} 00^{'}$	.8552
.7330	$42^{\circ} 00^{'}$	.6691	.7431	.9004	1.111	1.346	1.494	$48^{\circ} 00^{'}$	.8378
.7505	$43^{\circ} 00^{'}$	.6820	.7314	.9325	1.072	1.367	1.466	$47^{\circ} 00^{'}$	.8203
.7679	$44^{\circ} 00^{'}$	.6947	.7193	.9657	1.036	1.390	1.440	$46^{\circ} 00^{'}$	.8029
.7854	$45^{\circ} 00^{'}$	.7071	.7071	1.0000	1.0000	1.414	1.414	$45^{\circ} 00^{'}$	.7854
		cos y	sin y	cot y	tan y	csc y	sec y	y degree	y radians

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