# Math Projects Based on Trigonometry ••• segawa7/iStock/GettyImages

To help students learn trigonometry, consider hands-on projects that include the arts and sciences to make an engaging learning environment. Trigonometry-based math projects help to visually display concepts and applications of angles and principles. Discover the world of angles with projects based on fundamental principles that will fascinate students year after year.

## Trigonometry: The Basics

A project that shows trigonometry principles for beginning students requires at least a basic understanding of the subject. Draw three right triangles and label the angle and two sides that apply to the sine, cosine and tangent functions respectively. Student groups can draw X-Y graphs of the sine, cosine and tangent functions from zero to 360 degrees, setting the X axis as the angle. You can also show that ending with a multiple of 360 reveals that these functions repeat. In addition, groups can draw a unit circle with all known values of sine, cosine and tangent marked at the corresponding angles. Offer these ideas and challenge the students to come up with their own. The project results can serve as an introduction for younger students just starting out with the subject.

## Art with Trigonometry

The beauty of symmetry makes expressive art in this math project. Have students use at least six trigonometric functions (like sine, cosine and tangent) over a domain such as zero to 180 degrees to reveal the symmetry. They can use a graphing calculator to compare the functions visually. Have students conventionally plot each graph on oversized paper. Have students fill the symmetric parts with colors that stand out. For more advanced students, try circular patterns on polar graph paper instead of cartesian coordinates. The art and fun makes a strong impression with this trigonometry project.

## Rockets Trigonometry Project

Simple rocket construction requires a half-filled water bottle and a tire pump. Getting the rocket to go higher may require special fittings, but making a rocket helps with understanding trigonometric math-based principles. By launching rockets at a predetermined angle, students can calculate the height the rockets will reach, using a measuring tape and equations from trigonometry class. The actual construction of a rocket makes use of trigonometry as well but may be hard to incorporate.

## Measuring a Tall Building

Applied trigonometry means using the principles from the classroom to solve real-life problems. Students can, for example, find the height of their school building. This project starts with steps to determine of the angle at which the sun hits the building. A vertical stick will cast a shadow with the same angle as the building’s shadow. Measure the height of the stick and length of the shadow. Use the Pythagorean theorem to find the hypotenuse and the law of sines to find the angle of the sun hitting the building. Use the law of cosine with the discovered angle and the length of the building's shadow to solve for the height of the building.

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