Agreed. I was under the impression that the OP wanted to calculate on specific value.

To be honest I have little idea what the OP wants - it's one of those threads that got an interesting angle where the OP really didn't provide enough information to specify the question.

Somewhere else he mentions that he needs the answers every 15 degrees, well I presume he knows the values at 30, 45 and 60, he can work out the rest from sin(A-B) and sin(A+B) etc.. Without a calculator he needs to be able to do sqrt to compute sin(45) and sin(60).

Alternatively maybe he just needs the half angle formulas
http://www.intmath.com/analytic-trigonometry/4-half-angle-formulas.php
but there he would also have to be able to do sqrt without a calculator - another interesting thread.

 

The original question was on calculation of sin and cosine of an angle

I have never encountered a triangle that could not be bisected and thereby create two right triangles. Whether this would be the easiest method was not part of the original question, nor was it considered when giving my answer. If it is needed to argue an aspect of advanced mathematics not included in the OP's original question, then I will step aside, and let someone more inclined to such thing indulge themselves in that exciting internet pastime.

 

√∏e radians is an angle.

Not trying to upset you Kermit2, just that triangle information is not always available given an angular value. Frequently, its just an angle.

 

When I started college, they had just begun to allow calculators. In my Intro to Mechanical Engineering class the professor stated, "We decided there is no place you would need to make calculations that we could not send batteries.".

Funny thing, I had a solar powered TI-36 I purchased back then, some 30 years ago. It is still on my desk and used daily. So I might amend my professors statement, "Any place you have enough light to calculate, your solar powered calculator will work."

 

If you download the math<date>.zip file from here, it contains a file named BusinessCardMathTables.pdf that one might find useful. I keep a couple of those tables in my pocket for when I'm somewhere I need to do a calculation and don't have a calculator handy. This stuff was common for those of us who went to college in the 60's and before, but you sure get rusty if you haven't done it in a while -- do a few problems to realize how dependent you've become on your calculator or computer.

 

Don't know about you guys, but I'd whip out my trusty Eugene Dietzen Log-Log Duplex Deci-trig....slide rule. It's an analog table of logarithms.