Natural values of the trigonometric functions

Angle in	Angle in
Radians	Degrees	Sin	Cos	Tan	Cot	Sec	Csc
0	0	0	1	0	$\infty$	1	$\infty$
$\frac{\pi}{6}$	30	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{\sqrt{3}}{3}$	$\sqrt{3}$	$\frac{2\sqrt{3}}{3}$	$2$
$\frac{\pi}{4}$	$45$	$\frac{\sqrt{2}}{2}$	$\frac{\sqrt{2}}{2}$	1	1	$\sqrt{2}$	$\sqrt{2}$
$\frac{\pi}{3}$	60	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$	$\frac{\sqrt{3}}{3}$	2	$\frac{2\sqrt{3}}{3}$
$\frac{\pi}{2}$	90	1	0	$\infty$	0	$\infty$	1
$\pi$	180	0	-1	0	$\infty$	-1	$\infty$
$\frac{3\pi}{2}$	270	-1	0	$\infty$	0	$\infty$	-1
$2\pi$	360	0	1	0	$\infty$	1	$\infty$

Angle in	Angle in
Radians	Degrees	Sin	Cos	Tan	Cot
.0000	0	.0000	1.0000	.0000	Inf.	90	1.5708
.0175	1	.0175	.9998	.0175	57.290	89	1.5533
.0349	2	.0349	.9994	.0349	28.636	88	1.5359
.0524	3	.0523	.9986	.0524	19.081	87	1.5184
.0698	4	.0698	.9976	.0699	14.300	86	1.5010
.0873	5	.0872	.9962	.0875	11.430	85	1.4835
.1745	10	.1736	.9848	.1763	5.671	80	1.3963
.2618	15	.2588	.9659	.2679	3.732	75	1.3090
.3491	20	.3420	.9397	.3640	2.747	70	1.2217
.4863	25	.4226	.9063	.4663	2.145	65	1.1345
.5236	30	.5000	.8660	.5774	1.732	60	1.0472
.6109	35	.5736	.8192	.7002	1.428	55	.9599
.6981	40	.6428	.7660	.8391	1.192	50	.8727
.7854	45	.7071	.7071	1.0000	1.000	45	.7854
						Angle in	Angle in
		Cos	Sin	Cot	Tan	Degrees	Radians

You can create a table like this in Sage:

[fontsize=\scriptsize,fontfamily=courier,fontshape=tt,frame=single,label=\sage]

sage: RR15 = RealField(15)
sage: rads1 = [n*0.0175 for n in range(1,6)]
sage: rads2 = [0.0875+n*0.0875 for n in range(1,9)]
sage: rads = rads1+rads2
sage: trigs = ["sin", "cos", "tan", "cot"]
sage: tbl = [[eval(x+"(%s)"%y) for x in trigs] for y in rads]
sage: tbl = [[RR15(eval(x+"(%s)"%y)) for x in trigs] for y in rads]
sage: print Matrix(tbl)
[0.01750  0.9998 0.01750   57.14]
[0.03499  0.9994 0.03502   28.56]
[0.05247  0.9986 0.05255   19.03]
[0.06994  0.9976 0.07011   14.26]
[0.08739  0.9962 0.08772   11.40]
[ 0.1741  0.9847  0.1768   5.656]
[ 0.2595  0.9658  0.2687   3.722]
[ 0.3429  0.9394  0.3650   2.740]
[ 0.4237  0.9058  0.4677   2.138]
[ 0.5012  0.8653  0.5792   1.726]
[ 0.5749  0.8182  0.7026   1.423]
[ 0.6442  0.7648  0.8423   1.187]
[ 0.7086  0.7056   1.004  0.9958]

The first column are the values of $\sin(x)$ at $x\in \{0.01750, 0.03500, ... %0.05250, 0.07000, 0.08750, 0.1750, 0.2625, 0.7875\}$ (measured in radians). The second, third and fourth rows are the corresponding values for $\cos$, $\tan$ and $\cot$, respectively.