# How can I generate this exact table?

The TableForm[] is a trig table which shows sine, cosine and tangent values for integer angles from 0 degrees to 90 degrees in steps of 3 degrees.

I want to recreate the exact same table using Mathematica. I need to use TableForm[].

This is what I have so far:

TeXForm@TableForm[
Select[
Flatten[
Table[
{angle, sine, cosine, tangent},
{angle, 0, 90, 3},
{sine, N[Sin[0 Degree], 4], N[Sin[90 Degree], 4], angle},
{cosine, N[Cos[0 Degree], 4], N[Cos[90 Degree], 4], angle},
{tangent, N[Tan[0 Degree], 4], N[Tan[90 Degree], 4], angle}
],
1
],
IntegerQ[#[[3]]] && GCD[#[[1]], #[[2]]] == 1 &
]
]


I'm trying to manipulate code that I used for making another table so the last line:

IntegerQ[#[[3]]] && GCD[#[[1]], #[[2]]] == 1 &


Might be completely irrelevant. For the lines that show sine, cosine and tangent, I tried to start at 0 degrees, show 4 numbers (leading zeros don't count hence the values for angle 3 for sine and tangent), go up to 90 degrees, and I want it to go up in increments of 3 degrees.

Thank you for any help.

columnheadings = {"angle", "sine", "cosine", "tangent"};
vals = Table[{angle, N[Sin[angle Degree], 4], N[Cos[angle Degree], 4],
N[Tan[angle Degree], 4]}, {angle, 0 , 90, 3}];



TeXForm[t]


$$\begin{array}{cccc} \text{angle} & \text{sine} & \text{cosine} & \text{tangent} \\ 0 & 0 & 1.000 & 0 \\ 3 & 0.05234 & 0.9986 & 0.05241 \\ 6 & 0.1045 & 0.9945 & 0.1051 \\ 9 & 0.1564 & 0.9877 & 0.1584 \\ 12 & 0.2079 & 0.9781 & 0.2126 \\ 15 & 0.2588 & 0.9659 & 0.2679 \\ 18 & 0.3090 & 0.9511 & 0.3249 \\ 21 & 0.3584 & 0.9336 & 0.3839 \\ 24 & 0.4067 & 0.9135 & 0.4452 \\ 27 & 0.4540 & 0.8910 & 0.5095 \\ 30 & 0.5000 & 0.8660 & 0.5774 \\ 33 & 0.5446 & 0.8387 & 0.6494 \\ 36 & 0.5878 & 0.8090 & 0.7265 \\ 39 & 0.6293 & 0.7771 & 0.8098 \\ 42 & 0.6691 & 0.7431 & 0.9004 \\ 45 & 0.7071 & 0.7071 & 1.000 \\ 48 & 0.7431 & 0.6691 & 1.111 \\ 51 & 0.7771 & 0.6293 & 1.235 \\ 54 & 0.8090 & 0.5878 & 1.376 \\ 57 & 0.8387 & 0.5446 & 1.540 \\ 60 & 0.8660 & 0.5000 & 1.732 \\ 63 & 0.8910 & 0.4540 & 1.963 \\ 66 & 0.9135 & 0.4067 & 2.246 \\ 69 & 0.9336 & 0.3584 & 2.605 \\ 72 & 0.9511 & 0.3090 & 3.078 \\ 75 & 0.9659 & 0.2588 & 3.732 \\ 78 & 0.9781 & 0.2079 & 4.705 \\ 81 & 0.9877 & 0.1564 & 6.314 \\ 84 & 0.9945 & 0.1045 & 9.514 \\ 87 & 0.9986 & 0.05234 & 19.08 \\ 90 & 1.000 & 0 & \text{ComplexInfinity} \\ \end{array}$$

An alternative with dividing lines:

tt = Grid[Join[{columnheadings}, vals],
Dividers -> {All, {True, True, False}}, Frame -> True,
Spacings -> {1, .5}]


TeXForm[tt]


$$\begin{array}{|c|c|c|c|} \hline \text{angle} & \text{sine} & \text{cosine} & \text{tangent} \\ \hline 0 & 0 & 1.000 & 0 \\ 3 & 0.05234 & 0.9986 & 0.05241 \\ 6 & 0.1045 & 0.9945 & 0.1051 \\ 9 & 0.1564 & 0.9877 & 0.1584 \\ 12 & 0.2079 & 0.9781 & 0.2126 \\ 15 & 0.2588 & 0.9659 & 0.2679 \\ 18 & 0.3090 & 0.9511 & 0.3249 \\ 21 & 0.3584 & 0.9336 & 0.3839 \\ 24 & 0.4067 & 0.9135 & 0.4452 \\ 27 & 0.4540 & 0.8910 & 0.5095 \\ 30 & 0.5000 & 0.8660 & 0.5774 \\ 33 & 0.5446 & 0.8387 & 0.6494 \\ 36 & 0.5878 & 0.8090 & 0.7265 \\ 39 & 0.6293 & 0.7771 & 0.8098 \\ 42 & 0.6691 & 0.7431 & 0.9004 \\ 45 & 0.7071 & 0.7071 & 1.000 \\ 48 & 0.7431 & 0.6691 & 1.111 \\ 51 & 0.7771 & 0.6293 & 1.235 \\ 54 & 0.8090 & 0.5878 & 1.376 \\ 57 & 0.8387 & 0.5446 & 1.540 \\ 60 & 0.8660 & 0.5000 & 1.732 \\ 63 & 0.8910 & 0.4540 & 1.963 \\ 66 & 0.9135 & 0.4067 & 2.246 \\ 69 & 0.9336 & 0.3584 & 2.605 \\ 72 & 0.9511 & 0.3090 & 3.078 \\ 75 & 0.9659 & 0.2588 & 3.732 \\ 78 & 0.9781 & 0.2079 & 4.705 \\ 81 & 0.9877 & 0.1564 & 6.314 \\ 84 & 0.9945 & 0.1045 & 9.514 \\ 87 & 0.9986 & 0.05234 & 19.08 \\ 90 & 1.000 & 0 & \text{ComplexInfinity} \\ \end{array}$$

Another option would be to adjust the formatting in TeX.

• thank you so much!! this is a really dumb question but what about the borders and column bars? is there a way i can add it? – user130306 May 20 '19 at 4:55
• also how can i make it show 4 digits like for last value under sine column making it 1.000. and taking away the period in the first value under sine column? – user130306 May 20 '19 at 4:58
• @user130306 Oh sorry, to show 4 digits you can use, for example, N[Sin[angle Degree], 4] as you had it. – MelaGo May 20 '19 at 5:05
• @user130306 Regarding borders/divider lines - you can make a table with full control over grid lines using Grid; I will update the answer accordingly. However, I'm not sure how it carries over in TeXForm. – MelaGo May 20 '19 at 5:26

As in your image, this gives four significant digits except integers are kept exact.

nf = NumberForm[N@#, {6, 4 - Ceiling@Log10[N@#]}] &;

Off[NumberForm::iprf]

Framed[Grid[
Prepend[
Table[
{a, Sin[a Degree], Cos[a Degree], Tan[a Degree]},
{a, 0, 90, 3}] /.
x_?(NumericQ[N[#]] && Not[IntegerQ[#]] &) :> nf[x],
{"angle", "sine", "cosine", "tangent"}],
Dividers -> {All, {False, True}}],
FrameStyle -> Thick]