We know that the length of the contact point determines the ratio of leverage. In order to get accurate dial readings the length must be as specified by the manufacturer.
Changing the angle of the contact point changes the ratio just as if you had installed a somewhat shorter point. As a result, the readings on the dial will be higher than they should be.
To compensate for this cosine error it will be necessary to multiply the reading on the dial by the cosine of the angle between the contact point and the measuring surface.
How do you measure the angle? Most of us can intuitively judge an angle of 45° and, perhaps with a little less accuracy, an angle of 30°. Beyond that, we need help. A simple protractor like we used in grade school will suffice. Lay the straight edge on the measuring surface and, by eye, make a judgement of the angle. A few degrees one way or another won't be significant.
Where do you find the cosine? Use a scientific calculator or a printed chart.
Texas Instruments Scientific Calculator
Enter the value of the angle: for 20° enter "20" and press the COS (cosine) button. The display will read .9340 (allowing for rounding up).
Now it's simply a matter of multiplying the reading on your test indicator with this value.
For example: when the reading is .0006" you multiply .0006" x .9340 and the result is .00056"
This is just as expected. Your reading of .0006" was larger by .00004" than it should have been.
From this example you can see that angles of 20 degrees or less have relatively insignificant effects on the reading. But, when the angles are larger you'll be wise to make cosine error adjustments.
This same cosine error applies to all makes of test indicators regardless of contact point lengths and resolutions. Some Fowler test indicators feature "pear-shaped" contact points which compensate, in theory, for the cosine error. These may be a good choice if you frequently use a variety of measuring angles.
Interapid indicators pose a special problem. They're designed to work without cosine error at 12°. When setting up, use a protractor to make sure you're in the ball park. If you're off, then you'll have to compensate, just like the others. If the angle is 32° then the cosine will have to be of the difference between 32° and 12°, in other words 20°. Make the calculations as above.