Table for correcting scale problems
main page
1). Imagine that the object shown is the top of a (cylindrical) table leg or similar. You've decided that instead of having vertical legs, you want them to be at a slight angle. 
2). Select the leg and apply Object | Rotate -> Z ( 33 deg was used here) Rotating the whole leg has also made its end rotate so it is no longer horizontal (won't fit properly on the underside of the table) - so it needs to be adjusted.
3). Select the end face of the leg and apply Face | Rotate -> Z ( -33 deg .same angle as leg rotate, opposite direction) This makes the end face horizontal again, but distorts the cylinder (in one plane only), so it is no longer cylindrical.
4). To correct this distortion we need to scale the end face along the X axis only. With end face (still) selected from the previous op. apply Face | Scale -> X and drag to adjust.
5). Whilst eyeballing the scale op in (4) is often sufficient, using the data here ensures accurate correction of this problem. Here, whilst dragging the Face | Scale op, press the Tab key, which displays a data entry dialogue box. Enter 119.24% and click ok.
6). End result - horizontal top, leg cylindrical again.

What's this all about? - I hear people say - why should I
ever want to know how to do this sort of stuff :)

Probably right - however - imagine that you've put a new edgeloop around a cylinder - and rotated the loop, in a similar manner to the above example and ended up 'pinching' the cylinder - and you want to get it back to being cylindrical again.These figures will work for that situation as well :) - just do a vector scale along the relevant axis (using appropriate figure) and you'll have your rotated edgeloop and a 'true' cylinder.

Where did the 119.24% figure come from?

The expression used is this:

Cosecant (A) * 100 = Scaling Factor in %
A= Angle between the Cylinder Axis and the HORIZONTAL

So, in the above case, the cylinder was rotated 33 Deg from the Vertical or (90 - 33) Deg from the Horizontal (57 deg)

Look up 57 Deg and read off 119.24% -> this was the figure used.(It might be worth noting the scale factors for 30 deg and 45 deg - one's easy to remember and the other's worth remembering (imo) - the digits involved being the same as sq rt 2 (1.4142) - just a decimal place shift)
Edge loop correction
1). Cylinder with new edgeloop - after a connect operation (say) - could be an arm/leg or piece of machinery etc?
2). New loop after being rotated Z 45 deg.
3). Select the loop and apply Edge | Scale (Use RMB option to pick an axis) - in this case, define the axis by selecting the 2 verts that lie on the central Z plane of the cylinder. If you use LMB for selecting both verts you should see a vector similar to that shown.
4). Start dragging and press tab for the Numeric Input box - enter 141.42% as shown and ok.
5). Final result.
Pick the correct information from the table as before.
Table of scaling factors for correcting distorted end faces (and edgeloops) on angled cylinders etc

A = Angle between cylinder centreline and the HORIZONTAL.
A        scale %               A      scale %                A      scale %                A       scale %               A     scale %

1        5730.00              21       279.04               41      152.43                 61       114.34               81     101.25
2        2865.00              22       266.95               42      149.45                 62       113.26               82     100.98
3        1911.00              23       255.93               43      146.63                 63       112.23               83     100.75
4        1434.00              24       245.86               44      143.96                 64       111.26               84     100.55
5        1147.00              25       236.62               45      141.42                 65       110.34               85     100.38
6          956.70              26       228.12               46      139.02                 66       109.46               86     100.24
7          820.60              27       220.27               47      136.73                 67       108.64               87     100.14
8          718.50              28       213.01               48      134.56                 68       107.85               88     100.06
9          639.20              29       206.27               49      132.50                 69       107.11               89     100.02
10        575.88              30       200.00               50      130.54                 70       106.42

11        524.08              31       194.16               51      128.68                 71       105.76
12        480.97              32       188.71               52      126.90                 72       105.15
13        444.54              33       183.61               53      125.21                 73       104.57
14        413.36              34       178.83               54      123.61                 74       104.03
15        386.37              35       174.34               55      122.08                 75       103.53
16        362.80              36       170.13               56      120.62                 76       103.06
17        342.03              37       166.16               57      119.24                 77       102.63
18        323.61              38       162.43               58      117.92                 78       102.23
19        307.16              39       158.90               59      116.66                 79       101.87
20        292.38              40       155.57               60      115.47                 80       101.54
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