Lesson 1

Lesson 1: Foundations of Trigonometry

Focus

As mentioned in Module Introduction, trigonometry can be used to determine distances and angles when it is not feasible to measure them directly.

Stone arches in the shape of a semicircle are popular historic sites. Some of these are regularly repaired in order to preserve history. Repair of England’s Lune Aqueduct, similar to the arches pictured and first constructed in the 1700s, is currently planned. Measuring the heights at various angles inside the arches is an important part of the restoration. Later in this lesson you will see how trigonometry can help measure these heights.

In Lesson 1 you will learn about an extension of trigonometry that does not require right triangles and can be used for angles greater than 90°.

Outcomes

At the end of this lesson you will be able to

• describe how cosine, sine, and tangent are defined for angles greater than 90°
  
  
• determine the sign (positive or negative) of cosine, sine, and tangent for any angle without using your calculator
  
  
• state the number of solutions to a linear trigonometric equation, such as sin θ = 0.4

Lesson Questions

You will investigate the following questions:

• How can you use cosine, sine, and tangent for angles greater than 90°?

• How does the definition of cosine, sine, and tangent for angles greater than 90° affect the solution of equations?

Assessment

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

• completion of the Lesson 1 Assignment (Download the Lesson 1 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
  
  
• work under Project Connection

Self-Check activities are for your own use. You can compare your answers to suggested answers to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.