Introduction and basics in Part 1. Squares, Cubes and roots in Part 2. Here we cover trigonometry: sine, cosine and tangent. Not all slide rules have these scales, but when they do they are usually labeled as follows:

• S: sine
• T: tangent
• ST: sine & tangent

Notes on these scales:

Trig Scales

You don’t need both sine & cosine, since they are inverse every 1/4 circle or 90 degrees. That is, for any angle A in degrees, sin(A) = cos(90-A). That’s why slide rules don’t have a cosine scale – it’s not needed.

Knowing a few key values of sine enables one to quickly estimate many problems (like crosswinds when landing an airplane) in your head. No need for a slide rule, let alone a calculator.

• sin(0) = 0
• sin(30) = 0.5
• sin(45) = 0.707
• sin(90) = 1

For small angles, sine and tangent are almost the same. Thus many slide rules have an shared ST scale for both, for small angles – typically less than about 5*. Exactly how close are sine and tangent for small angles?

• 2 sig figs: 15* – sin & tan differ by the 2nd sig fig
  • sin(15*) = 0.259
  • tan(15*) = 0.268
• 3 sig figs: 2* – sin & tan differ by the 3rd sig fig
  • sin(3*) = 0.0523
  • tan(3*) = 0.0524