Trigonometry (I)

Grade 11 · Mathematics

Semester 2 | Period 4 | Week 23

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Subject: Mathematics

Semester: 2

Period: 4

Week: 23

Week 23

Class: Grade 11

Age: 16 years

Duration: 40 minutes per period (5 periods)

Subject: Mathematics

Topic: Trigonometry (I)

Focus: Derivation of Sine Rule and Its Application, Derivation of Cosine Rule and Its Application

Specific Objectives:

By the end of the lesson, students should be able to:

  1. Derive the sine rule and apply it in solving problems.
  2. Derive the cosine rule and apply it in solving problems.
  3. Understand the relationship between angles and sides of a triangle using sine and cosine rules.

 

Instructional Techniques:

  • Question and Answer
  • Guided Demonstration
  • Discussion
  • Practice Exercises
  • Use of Charts and Visual Aids

 

Instructional Materials:

  • Acute angle chart
  • Obtuse-angled triangle chart
  • Whiteboard and markers
  • Rulers and protractors
  • Trigonometry tables for reference
  • Worksheet for sine and cosine rule problems

 

Period 1 & 2: Derivation of the Sine Rule and Its Application

Presentation:

Step

Teacher's Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of the sine rule in a triangle. Displays a chart of an acute-angled triangle.

Students observe the chart and listen to the teacher’s explanation.

Step 2 - Derivation of the Sine Rule

Guides students to identify corresponding angles and sides in a triangle. Derives the sine rule from the law of sines: a/sinA = b/sinB = c/sinC.

Students follow the teacher’s steps and take notes on the derivation.

 

       3. Solve for side c in triangle ABC where side a = 15 cm, side b = 20 cm, and angle C = 120°.

       4. Solve for angle A in triangle ABC where side a = 7 cm, side b = 8 cm, and side c = 9 cm.

       5. Calculate side a in a triangle where side b = 11 cm, side c = 13 cm, and angle C = 90°.

ASSIGNMENT (5 tasks):

  1. Solve for angle B in triangle ABC where sides a = 10 cm, b = 15 cm, and angle C = 120°.
  2. Derive the cosine rule from the law of cosines and provide examples of its application.
  3. Solve for side b in a triangle where side a = 9 cm, side c = 14 cm, and angle C = 60°.
  4. If side a = 5 cm, side b = 7 cm, and angle A = 60°, find angle B using the cosine rule.
  5. Provide a real-life scenario where the cosine rule can be applied.

 

Period 5: Consolidation and Practice

Presentation:

  • Review the sine and cosine rules.
  • Engage students in solving combined problems that require both sine and cosine rules.
  • Ensure students understand when to use each rule based on the given information.

EVALUATION (5 exercises):

  1. Solve for side c in triangle ABC using both the sine and cosine rules.
  2. Solve for angle A in a triangle where sides a = 12 cm, b = 10 cm, and angle C = 60°.
  3. Use both sine and cosine rules to solve a triangle where angles A = 40°, B = 60°, and side a = 8 cm.
  4. Derive both the sine and cosine rules from the basic principles of trigonometry.
  5. Solve a real-life problem using either the sine or cosine rule.