Polytechnic 1st semester mathematics chapter 1 trigonometry

Polytechnic 1st Semester Mathematics – Unit 1

Chapter 1: Trigonometry (त्रिकोणमिति)

Welcome to D2D Pathshala Trigonometry notes for BTER Polytechnic Semester 1 Mathematics. This page has easy, exam-oriented theory, formulas, solved examples, memory tips, and video lectures.

---

1. Introduction — What is Trigonometry?

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles. It comes from Greek words:

• Trigonon meaning “triangle”
• Metron meaning “measure”

It’s most useful for solving right triangles, modeling periodic phenomena, and in engineering applications.

📺 Video – Introduction & Basic Ratios

---

2. Angle Measurement Systems

Angles can be measured in three systems:

• Sexagesimal (Degree system):
  Full revolution = 360°, 1 right angle = 90°, 1° = 60′, 1′ = 60″
• Centesimal (Grades):
  Full revolution = 400g, 1 right angle = 100g
• Circular (Radian measure):
  Angle based on arc length.
  1 radian = arc length / radius
  Full revolution = 2π radians, 1 right angle = π/2 radians

Conversions

• Degrees → Radians: θ (rad) = θ (°) × π / 180
• Radians → Degrees: θ (°) = θ (rad) × 180 / π

📺 Video – Angle Measurement & Conversions

---

3. Trigonometric Ratios – Definitions

In a right triangle with angle θ:

• sin θ = Opposite / Hypotenuse
• cos θ = Adjacent / Hypotenuse
• tan θ = Opposite / Adjacent
• cot θ = Adjacent / Opposite
• sec θ = Hypotenuse / Adjacent
• cosec θ = Hypotenuse / Opposite

Mnemonic (to remember ratios): SOH CAH TOA (Sin = Opp/Hyp, Cos = Adj/Hyp, Tan = Opp/Adj)

📺 Video – Trigonometric Ratios

---

4. Fundamental Trigonometric Identities

These identities are used most often in exams and simplifications:

• sin²θ + cos²θ = 1
• 1 + tan²θ = sec²θ
• 1 + cot²θ = cosec²θ
• tan θ = sin θ / cos θ
• cot θ = cos θ / sin θ

Remember: These identities help you transform and simplify expressions during problem solving.

📺 Video – Trigonometric Identities & Proofs

---

5. Solved Exam Oriented Examples

Example 1

Given: Evaluate sin 30°, cos 60°, tan 45°

Solution:

• sin 30° = 1/2
• cos 60° = 1/2
• tan 45° = 1

Answer: 1/2, 1/2, 1

Example 2

Find: Simplify sin²θ + cos²θ

Solution: Using identity: sin²θ + cos²θ = 1

Answer: 1

---

6. Practice Questions & Answers

Q1. Convert 120° to radians.

Ans: 120° × π/180 = (2π/3) rad

Q2. If sin θ = 3/5, find cos θ and tan θ (in right triangle).

Ans: cos θ = 4/5, tan θ = 3/4 (Triangle sides: 3, 4, 5)

Q3. Verify 1 + tan²θ = sec²θ

Ans: Identity holds from fundamental formulas

---

Download Complete Trigonometry Notes PDF

📥 Click here to download Trigonometry Notes (PDF)

---

💡 Study Tips:
✔ Master basic ratios first → SOH CAH TOA
✔ Learn identities by heart using short tricks
✔ Watch each video after reading theory
✔ Do practice problems daily

Best of luck for your Polytechnic exam! 📘✨ — D2D Pathshala