When surveyors use trigonometric functions in their calculations, seldom do they realize the ranges of values that trig functions can take and how and when the sign of the values change to identical but negative values. This is better understood by looking at the curves or plots of the basic three functions: sine, cosine, and tangent. To counter the often-encountered problem of selecting the wrong function, a discussion is held on the values at various intervals around the circle for these three functions. The emphasis is to visualize what the answer will be approximate as a check on oneself or others. This knowledge is then tied to the calculation of latitudes and departures, concepts that are vital to passing the FS exam as well as various levels of CST tests. Again, by visualizing the sine and cosine functions approximate answers can be determined as a quality assurance check on the computed values. Don’t know what latitudes and departures are? You’ll find it explained in any textbook, and they will be the standard terms for what many people know as the ∆ northing and ∆ easting of a line. We then move on to the mathematical concepts underlying the computation of standard deviation (or standard error). This is also prime exam material as a straightforward calculation with a given dataset, but can also be used as a tool to evaluate the quality of a group of measurements and sometimes individual measurements in a group. This data analysis aspect is important to those planning on taking the FS exam. Running time 25 minutes.
You will learn…
- The shapes of the trigonometric functions: sine, cosine, and tangent
- The importance of learning the values of the functions for representative angles, and the algebraic signs to help the surveyor “know” the answer, actually an estimate, before actually doing the calculation
