Trigonometry and Statistics MATH 1513

Upon successful completion of this course, the student will be able to:

• Use basic algebraic rules and operations.
• Rearrange formulae used in geomatics.
• Solve line intersection problems.
• Formulate and solve elementary geometric properties of circles.
• Solve right-angle triangles using trigonometry. Use right-angle trigonometry to solve applied surv
• Use radian measure in the solution of surveying problems involving circular arcs.
• Use the sine and cosine laws for solving oblique triangles.
• Apply the sine and cosine laws to elevation problems and traverses.
• Carry out the simplification of trigonometric expressions using trigonometric identities.
• Solve simple trigonometric equations.
• Use statistical parameters in reducing surveying measurements.
• Apply area formulae to problems such as finding the area contained in a traverse and the area contained within a lot with an irregular boundary.
• Apply volume formulae to problems such as cut and fill.
• Solve right-angled spherical triangles.
• Solve oblique spherical triangles.
• Use spherical triangles for determining azimuth and bearing.
• Produce histograms and other statistical plots from raw, observed survey data.
• Calculate measures of central tendency and variation such as mean, median, variance and standard deviation from geomatics measurement data.
• Define the basic laws of probability.
• Connect probability to the randomness of error in measurement.
• Define continuous and discrete probability distributions, such as the normal, binomial, student's-t, chi-square and F-distribution, and calculate their mean and variance.
• Use the normal distribution to determine probabilities of observing defined ranges of measurement in geomatics projects.
• Estimate confidence intervals for large and small samples and apply them to engineering and cadastral surveys and the analysis of error in least-squares adjustments.
• Conduct various hypothesis tests, including mean, variance, and correlation, and recognize the associated Type I and II errors.
• Investigate error propagation in geomatics calculations.
• Calculate the principal parameters of bivariate data, that is, the correlation coefficient and variance-covariance matrices, and relate them to adjustment of parameters.

Effective as of Fall 2024