Mathematics - Senior Secondary 1 - Trigonometry I

Trigonometry I

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Term: 3rd Term

Week: 5
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Trigonometry I

SPECIFIC OBJECTIVES

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

  1. Define and identify basic trigonometric ratios (sine, cosine, and tangent) in right-angled triangles.
  2. Identify trigonometric ratios of special angles: 30°, 45°, and 60°.
  3. Derive trigonometric ratios of 30°, 45°, and 60° from standard triangles.
  4. Use trigonometric ratios to solve problems involving missing sides and angles of right-angled triangles.

 

INSTRUCTIONAL TECHNIQUES

  • Question and answer
  • Guided demonstration
  • Group activity
  • Step-by-step problem solving
  • Real-life applications

 

INSTRUCTIONAL MATERIALS

  • Charts showing right-angled triangles
  • Cutout shapes of 30°, 45°, and 60° triangles
  • Rulers, pencils, and protractors
  • Graph sheets and mathematical sets
  • Worksheets for derivations and exercises

 

PERIOD 1 & 2: Introduction to Trigonometric Ratios

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 – Introduction

Introduces the topic by showing a chart of a right-angled triangle. Defines sine, cosine, and tangent in terms of opposite, adjacent, and hypotenuse.

Students observe the chart and copy definitions.

Step 2 – Identifying Ratios

Highlights how sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent.

Students take notes and ask questions.

Step 3 – Using Chart to Identify Ratios

Demonstrates with chart how each ratio applies to angles within the triangle. Emphasizes position of angle.

Students identify each side of triangle relative to the given angle.

Step 4 – Introduction to Special Angles

Introduces angles 30°, 45°, and 60°. Explains their importance in trigonometry.

Students write down the angles and their relevance.

Step 5 – Real-Life Connection

Discusses real-world applications of trigonometric ratios (e.g., construction, navigation).

Students contribute examples from their daily experiences.

NOTE ON BOARD:

  • sin(θ) = opposite/hypotenuse
  • cos(θ) = adjacent/hypotenuse
  • tan(θ) = opposite/adjacent

 

EVALUATION (5 Exercises):

  1. Define sine, cosine, and tangent.
  2. What are the sides used to form each trigonometric ratio?
  3. Write down the trigonometric ratios of a right-angled triangle.
  4. In a triangle where angle A = 30°, opposite = 3cm, hypotenuse = 6cm, find sin(A).
  5. List three real-life applications of trigonometric ratios.

 

CLASSWORK (5 Questions):

  1. Label the sides of a right-angled triangle given angle θ.
  2. Calculate sin(30°) using a triangle with opposite = 1, hypotenuse = 2.
  3. Find cos(60°) using appropriate sides.
  4. Derive tan(45°) from a triangle.
  5. Describe what each ratio tells us about the triangle.

 

ASSIGNMENT (5 Tasks):

  1. Draw a right-angled triangle and label sides for an angle of 45°.
  2. Explain the meaning of the term "trigonometric ratio."
  3. Construct a triangle with 60° and calculate all three ratios.
  4. Describe how trigonometry is used in architecture.
  5. Research and list the values of sin(30°), cos(60°), and tan(45°).

 

PERIOD 3 & 4: Derivation of Trigonometric Ratios of 30°, 45°, 60°

PRESENTATION

Step

Teacher’s Activity

Student’s Activity

Step 1 – Review

Reviews previous lessons and introduces triangle construction.

Students participate and ask questions.

Step 2 – Constructing Special Triangles

Guides students in constructing 30°-60°-90° and 45°-45°-90° triangles using rulers and protractors.

Students construct triangles with teacher guidance.

Step 3 – Deriving Ratios

Guides students in calculating sin, cos, and tan for each angle from the triangle sides.

Students perform calculations and compare answers.

Step 4 – Chart Comparison

Presents a chart with standard trigonometric values and asks students to compare.

Students confirm their results using the chart.

Step 5 – Practice Exercises

Provides more problems involving solving triangle side lengths using derived ratios.

Students solve problems independently or in pairs.

NOTE ON BOARD:

  • sin(30°) = 1/2
  • cos(60°) = 1/2
  • tan(45°) = 1
  • Derived using known right-angled triangles.

 

EVALUATION (5 Exercises):

  1. Derive sin(30°) from triangle sides.
  2. Calculate cos(60°) using constructed triangle.
  3. What is tan(45°) and why?
  4. Compare student-derived ratios with standard values.
  5. State two reasons for learning trigonometric ratios.

 

CLASSWORK (5 Questions):

  1. Construct and label a 45°-45°-90° triangle.
  2. Derive all three trigonometric ratios from it.
  3. What type of triangle is used for 30° and 60°?
  4. Construct triangle and find sin(60°), cos(30°), and tan(60°).
  5. Draw a table comparing student-derived and standard values.

 

ASSIGNMENT (5 Tasks):

  1. Derive the trigonometric ratios of 30°, 45°, and 60° using constructed triangles.
  2. List the exact values of sin, cos, and tan for these angles.
  3. Research practical uses of trigonometry in surveying.
  4. Solve for missing sides in a triangle where one side and an angle are known.
  5. Draw a mind map showing connections between angles, ratios, and triangle types.

 

PERIOD 5: Review and Application

PRESENTATION

  • Review all trigonometric ratios discussed during the week.
  • Reinforce understanding with blackboard examples and quick mental exercises.
  • Discuss frequently made errors and misconceptions.
  • Address students’ questions and clarify doubts.

 

EVALUATION

  1. Conduct a mini quiz with short answers.
  2. Observe student constructions for accuracy.
  3. Assess participation and problem-solving in class.

Provide detailed feedback on assignments and classwork.