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Wndsn Quadrant Telemeter Tutorials

Making the most out of our graphical telemetry computers.

Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses.

Find a Tangent with the Sine Quadrant

Level: Advanced

On the Sine Quadrant, we don't have a dedicated tangent scale, what we do have is a tangent chord (the straight line joining the ends of the arc from 0 to 90 degrees). Here is how to use it, and a trick to avoid complicated calculations.

The procedure

  • Using the string, we set the angle for which we want to obtain the tangent.
  • We recall that the sine of an angle is read on the vertical scale (in base 60) and the cosine on the horizontal scale (also in base 60). Now recall that tan = sin/cos (or rise over run).
  • We then read sin/cos on the tangent chord.
  • Or, we slide along the string until we find an easier to calculate pair of values.
  • If we need a decimal fraction, move vertically along 10cos and directly read the value as tenths.

Note that we can read the correct value anywhere along the string.

If the cotangent is what we are after, we recall that cot = cos/sin, hence we simply have to flip the equation.

Example 1

Computing the tangent of 58° on the Sine Quadrant.

Computing the tangent of 58° on the Sine Quadrant.

  1. On the chord, tan(58°) is 37/23.
  2. Sliding along the string, we get 40/25 for an even fraction.
  3. To further simplify, go down vertically from the cosine scale at the 10 mark.
  4. The string crosses the grid at a decimal value of 16/10 for tan(58°) = 1.6.

Example 2

Computing the tangent of 32° on the Sine Quadrant.

Computing the tangent of 32° on the Sine Quadrant.

  1. The value of tan(32°), read in tenths down from the cosine scale is about 6/10 = 0.6.
  2. By finding a suitable value pair of sin/cos, we can significantly enhance the accuracy and precision of our result: 25/40 = 5/8 = 0.625 ... which we can still easily calculate in our head.

Note that this is a straightforward and transparent procedure; you don't have to look up the result to confirm, instead the more precise you draw the string and identify a suitable sin/cos pair, the higher the accuracy and precision of the result.

See also:

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