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Lesson Plans Library 10-12 > Discovering Math
Discovering Math - Concepts in Precalculus I: Trigonometry
Discovering Math - Concepts in Precalculus I: Trigonometry
Grade level: 10-12 Subject: Discovering Math Duration: 3 class periods
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Objectives | Materials | Procedures | Evaluation | Vocabulary | Academic Standards | Credit 		 print this lesson plan
 



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Objectives
Students will
  • Study Islamic achievements in mathematics.
  • Calculate angles and distances using the Law of Sines and the Law of Cosines.
  • Apply right-triangle trigonometry to find distances.
  • Calculate angles and distances on the sphere using the spherical Law of Sines.
Materials
  • Discovering Math: Precalculus I: Trigonometery program
  • Computer with Internet access
  • Calculators
Procedures
  1. Begin the lesson by having students view Concepts in Precalculus I: Trigonometry.

  2. Have them research Islamic contributions to mathematics using print and Web resources. The following Web sites are a good starting point:
  3. Ask students to summarize their findings by writing a one-page report.

  4. Have students choose partners to share their reports and answer any questions. Then have students summarize their partners’ reports for the class, including at least three interesting facts.

  5. Review the Law of Cosines. Give examples of calculating angles and side lengths. Allow students time to practice.

  6. Review the Law of Sines. Give examples of calculating angles and side lengths. Allow students time to practice.

  7. Give examples of calculating angles of right triangles given side lengths using trigonometric identities. Allow students time to practice.

  8. Have each student choose three international cities. Using print or Internet resources, have them research two of the distances between the cities and the angle between those two paths. Students will calculate the distance between the other two cities using the Law of Cosines.

  9. Review the spherical Law of Sines. Give examples of calculating angles and side lengths. Allow students time to practice.

  10. Have students choose a different set of three international cities and research two of the angles and one of the distances between the cities. Students will calculate another distance using the spherical Law of Sines.

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Evaluation
Use the following three-point rubric to evaluate students' work during this lesson.
  • Three points: Students wrote complete reports with all the requested information; clearly demonstrated the ability to calculate angles and lengths of triangles using the Law of Sines, the Law of Cosines, and the spherical Law of Sines.
  • Two points: Students wrote reports with some of the requested information; demonstrated some ability to calculate angles and lengths of triangles using the Law of Sines, the Law of Cosines, and the spherical Law of Sines.
  • One point: Students wrote incomplete reports; did not demonstrate the ability to calculate angles and lengths of triangles using the Law of Sines, the Law of Cosines, and the spherical Law of Sines.

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Vocabulary
Andalusia
Definition: A region of the Muslim empire in southern Spain
Context: Seville and Cadiz were cities in Andalusia.

Law of Cosines
Definition: A formula that gives the length of a side of a triangle in terms of the opposite angle and the lengths of the other two sides
Context: If you know the distance from your house to two other locations, and you know the angle the paths make at your house, the Law of Cosines will help you find the distance between the other two locations.

Law of Sines
Definition: A formula that relates the lengths of sides of a triangle to the sines of the opposite angles
Context: If you know any side of a triangle and the measure of the angle opposite that side, apply the Law of Sines to find information about the other sides and angles.

qibla
Definition: The direction one must turn to face Mecca
Context: Devout Muslims need an accurate qibla to face when praying.

spherical trigonometry
Definition: The process of finding relationships between angles and sides of polygons on a sphere
Context: Because the Earth’s surface is not a plane, spherical trigonometry must be applied to give accurate measurements.

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Academic Standards
National Council of Teachers of Mathematics (NCTM)
The National Council of Teachers of Mathematics provides guidelines for teaching mathematics in grades K–12 to promote mathematical literacy. To view the standards, click here
This lesson plan addresses the following national standards:
  • Use trigonometric relationships to determine lengths and angle measures.
  • Use geometric models to gain insights into, and answer questions in, other areas of mathematics.
  • Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.

Mid-continent Research for Education and Learning (McREL)
McREL’s Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education addresses 14 content areas. To view the standards and benchmarks, click here
This lesson plan addresses the following national standards:

  • Mathematics: Understands and applies basic and advanced properties of functions and algebra; understands and applies basic and advanced properties of the concepts of geometry; uses trigonometric ratio methods to solve mathematical and real-world problems.
  • History: Understands how Islamic civilization contributed to mathematics.

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