I looked on Google. There is a used copy of the 11th edition of Standard Mathematical Tables available for under 6 dollars. My edition is the 12th, but it has the same awful brown hardcover. I presume it has virtually the same trig tables on almost the same pages.
So I looked more carefully at my edition. I was wrong yesterday; the table of sines, cosines, tangents, and cotangents only runs from pages 93 through 116. In one sense, it provides more than you want because it gives their value to four decimal places for each minute of a degree from 0 to 60. In another sense, it provides less than you want because it only runs from 0 degrees to 44 degrees 60 minutes. Of course that is all you need if you are prohibited by religion from using a hand calculator. And it will firmly persuade you that the trig functions represent numbers (or, to be more modern in terminology, represent real numbers that can be approximated by rational numbers to any level of accuracy required).
Why is that all you need? Because, working in degrees,
[MATH]0 \le \theta \le 45 \implies sin(\theta) = cos(90 - \theta) \text { and } cos(\theta) = sin(90 - \theta).[/MATH]
So if you need the sine of 60 degrees, you just look up the cosine of 30 degrees. That comes right out of the geometric definition of sine and cosine in terms of right triangles. And it explains the similarity of the names.
If you are willing to waste paper and ink, you can get a desktop computer to print out a table of sines and cosines for 0 to 360 degrees; nowadays you do not need a book; you can do it yourself
What I suspect would really help you is to go back and work out for yourself the relationship between the right angle definition and unit circle definitions of the sine and cosine of an arbitrary theta greater than 0 degrees but less than 90, of theta plus 90 degrees, of theta plus 180 degrees, and theta plus 270 degrees. You will find that the circle definition merely affects the signs of the functions, not their magnitude.
And then do in a right triangle the geometry of the sum of angle fotmulas. The other trig functions are just elaborations of sine and cosine and the sine and cosine just represent shifts in the same graph. If you fully feel the sine curve and its connection to the other functions, it becomes mechanics.
Now to understand all this in terms of the modern infinite series definitions is probably easier algebraically, but you lose any connection to a concrete geometric object that you can see.
