lesson 3

1. Revision of Trignometry

Trigonometry Revision Notes

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🔹 Purpose of This Lesson

This lesson is designed to revise all the important concepts of trigonometry covered in this course.

Go through these notes carefully before attempting practice problems or the final quiz.

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🔹 1. Right-Angled Triangle Basics

• A right-angled triangle has one angle equal to 90°

• Trigonometry mainly works with right-angled triangles

• The sides of a triangle depend on the angle chosen

Key idea:

• Longest side is always opposite the right angle

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🔹 2. Trigonometric Ratios

Trigonometric ratios relate the angles of a triangle to the lengths of its sides.

Main Ratios:

• sin θ = Opposite / Hypotenuse

• cos θ = Adjacent / Hypotenuse

• tan θ = Opposite / Adjacent

Easy Memory Trick:

SOH – CAH – TOA

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🔹 3. Trigonometric Identities

Trigonometric identities are formulas that are always true.

Important Identities:

• sin²θ + cos²θ = 1

• tan θ = sin θ / cos θ

Reciprocal Pairs:

• sin ↔ cosec

• cos ↔ sec

• tan ↔ cot

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🔹 4. Standard Trigonometric Values

Standard values are fixed values of sin, cos, and tan for common angles.

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🔹 5. Heights and Distances (Applications)

In real-life problems:

• Height → opposite side

• Distance on ground → adjacent side

• Angle of elevation → given angle

Most problems use:

• tan θ = Height / Distance

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🔹 6. Steps to Solve Trigonometry Problems

1️⃣ Draw or imagine the triangle
2️⃣ Mark the given angle
3️⃣ Identify known and unknown sides
4️⃣ Choose the correct ratio
5️⃣ Substitute values
6️⃣ Solve carefully

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🔹 7. Common Mistakes to Avoid

• Mixing up opposite and adjacent sides

• Choosing the wrong ratio

• Forgetting standard values

• Skipping steps

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✅ Lesson 3 Key Takeaway

✔ All important trigonometry concepts revised
✔ Formulas and values summarized
✔ Ready to solve problems confidently