Lesson 3

Lesson 3: Trigonometry Without Technology

Focus

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Bridges have always been needed to cross rivers and ravines. Bridges require sturdy trusses. The exact origin of the truss web, made up of identical repeating triangles, is unclear. Today, many other types of trusses exist. Triangles are one element all the different types of trusses have in common. You probably don’t have to look hard to see the triangles that make up the truss bridge shown in the photo.

In 1848, James Warren obtained a British patent for a design of repetitive equilateral triangles that could support a roadbed on either its top or bottom dimension. Warren's name became synonymous with this form of truss design.

How did the mathematicians and engineers who worked on bridges solve trigonometric equations without calculators? The vast majority of them used tables of values. One of the oldest known tables of values was created by the Greek astronomer and mathematician Hipparchus (ca. 190 BC to 120 BC). How were those tables created?

This lesson will help you understand how to calculate the cosine, sine, or tangent of a number of special angles without a calculator.

Outcomes

At the end of this lesson you will be able to

• determine, without the use of technology, the cosine, sine, or tangent of 0°, 30°, 45°, 60°, and 90° angles, and their reflections in the other three quadrants of the Cartesian plane
  
  
• determine the cosine, sine, or tangent of angles given the coordinates of a point on the terminal arm

Lesson Question

You will investigate the following question:

• How can the cosine, sine, or tangent of an angle be determined without technology?

Assessment

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 2 Glossary Terms and Formula Sheet