Trigonometry is a very useful area of mathematics. The buildings you see standing, the sounds you hear and so many other aspects of your daily life are possible because of the existence of trigonometric principles. Many students in schools across the world must learn trigonometry as a part of the math curriculum. There are several real world projects that can make learning "trig" easier.
Astronomy and Trigonometry
Even the stars that light up the night sky show trigonometric principles at work. For this project, an instructor would simply instruct his students to observe the sky at night and look for certain constellations, such as Orion's Belt and the Big Dipper, then try to measure the angles of various parts of each constellation, such as the angle of the handle of the Big Dipper. The instructor would also request that students bring in their data and give the students math problems related to the angles and distances of the constellations.
Trigonometry in Famous Landmarks
Trigonometry in buildings and famous structures is the focus of this project. The instructor would use various landmarks, such as the pyramids of Giza and the Gateway Arch in St. Louis, Missouri, and have students perform trigonometric calculations based on the actual measurements of these monuments. The students could calculate the height of the pyramids given only the lengths of the base and sides, or they could calculate the curve of the Gateway Arch using sine, cosine and tangent functions.
Trigonometry and Waves
Sound and light waves are primarily studied mathematically using trigonometric concepts. In this project, an instructor would play popular music at different speeds and volume levels, then demonstrate how trigonometry can be used to calculate the wavelength and amplitude of the sound waves. The instructor would then assign problems to the class based on the music studied in class. A similar project could be done using a small tank of water to simulate ocean waves.