Geologic context:
Waves (ocean and seismic), dunes and wind, subduction zones, strike and dip, compass directions, and many more...

Trigonometry and Angles

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What's so hard about angles and trigonometry?

An understanding of angles and the ability to manipulate trigonometric expressions is essential for the introductory geoscience student. Geoscientists use both of these concepts in numerous applications, from coastal geology to mineralogy to geologic mapping. Helping students to develop the tools they need to understand these important concepts can be challenging. Most college students have learned about trigonometry at some point in their high school career (remember "soh, cah, toa? sin = opposite/hypotenuse..."); however, moving beyond the abstract mathematics to application is often difficult for the student.

Teaching Strategies: Ideas from Math Education

Put quantitative concepts in context

Trigonometry and angles are used in a wide variety of geoscience topics, including:
Waves refracting as they approach shore. Details

Use multiple representations

Because everyone has different ways of learning, mathematicians have defined a number of ways that quantitative concepts can be represented to individual students. Below are some ways that angles and their relationship to trigonometry are used in geoscience concepts.

Use technology appropriately

Students have any number of technological tools that they can use to better understand quantitative concepts -- from the calculators in their backpacks to the computers in their dorm rooms. Students can make use of these tools to understand both right triangle geometry and trigonometric functions.

Work in groups to do multiple day, in-depth problems

Mathematicians also indicate that students learn quantitative concepts better when they work in groups and revisit a concept on more than one day. Therefore, when discussing quantitative concepts in entry-level geoscience courses, have students discuss or practice the concepts together. Also, make sure that you either include problems that may be extended over more than one class period or revisit the concept on numerous occasions.

Geoscience concepts reinforce trigonometric functions numerous times within one introductory course. Topics include angle of repose, wave refraction, the behavior of seismic waves in the Earth and measuring strike and dip. A detailed discussion is necessary when the concept is first introduced and some mathematical review will likely be necessary. However, when another topic related to trigonometry comes up, remind students of topics where the same mathematical skill is useful. Students are more likely to retain mathematical material when they see connections among topics.

Teaching Materials and Exercises

Student resources

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