CLASS 10 MATHEMATICS
Introduction to Trigonometry
COMPLETE PREMIUM NOTES
# Section Content
1 Full Chapter Notes Concepts, definitions, right triangle, ratios
2 Formula Sheet All formulas, identities, standard values
3 Solved Examples Step-by-step solutions with explanation
4 Important Q&A Exam-style questions with full answers
, SECTION 1 — FULL CHAPTER NOTES
1.1 What is Trigonometry?
Trigonometry is a branch of mathematics that studies the relationship between the angles and sides
of a right-angled triangle. The word comes from Greek: trigonon (triangle) + metron (measure). It is
widely used in engineering, physics, architecture, and navigation.
1.2 Right-Angled Triangle
In a right-angled triangle with angle θ:
• Hypotenuse (H) — the longest side, opposite the right angle (90°)
• Perpendicular / Opposite (P) — the side opposite to angle θ
• Base / Adjacent (B) — the side adjacent to angle θ
■ Memory Tip: Always label the triangle first before solving any problem.
1.3 Trigonometric Ratios
There are 6 trigonometric ratios for an angle θ in a right triangle:
Ratio Full Name Formula Reciprocal of
sinθ Sine P/H cosecθ
cosθ Cosine B/H secθ
tanθ Tangent P/B cotθ
cosecθ Cosecant H/P sinθ
secθ Secant H/B cosθ
cotθ Cotangent B/P tanθ
■ Memory Trick (SOH-CAH-TOA): Sin = Opposite/Hypotenuse | Cos = Adjacent/Hypotenuse | Tan =
Opposite/Adjacent
1.4 Relationship Between Ratios
• tanθ = sinθ / cosθ
• cotθ = cosθ / sinθ
• sinθ × cosecθ = 1 → cosecθ = 1/sinθ
• cosθ × secθ = 1 → secθ = 1/cosθ
• tanθ × cotθ = 1 → cotθ = 1/tanθ
1.5 Trigonometric Identities
These are equations that are true for all values of θ:
Identity 1: sin²θ + cos²θ = 1 (derived from Pythagoras theorem)
Identity 2: 1 + tan²θ = sec²θ
Identity 3: 1 + cot²θ = cosec²θ
■ Tip: These identities are used to prove expressions and simplify problems. Memorize all three —
they appear in nearly every board exam!
Introduction to Trigonometry
COMPLETE PREMIUM NOTES
# Section Content
1 Full Chapter Notes Concepts, definitions, right triangle, ratios
2 Formula Sheet All formulas, identities, standard values
3 Solved Examples Step-by-step solutions with explanation
4 Important Q&A Exam-style questions with full answers
, SECTION 1 — FULL CHAPTER NOTES
1.1 What is Trigonometry?
Trigonometry is a branch of mathematics that studies the relationship between the angles and sides
of a right-angled triangle. The word comes from Greek: trigonon (triangle) + metron (measure). It is
widely used in engineering, physics, architecture, and navigation.
1.2 Right-Angled Triangle
In a right-angled triangle with angle θ:
• Hypotenuse (H) — the longest side, opposite the right angle (90°)
• Perpendicular / Opposite (P) — the side opposite to angle θ
• Base / Adjacent (B) — the side adjacent to angle θ
■ Memory Tip: Always label the triangle first before solving any problem.
1.3 Trigonometric Ratios
There are 6 trigonometric ratios for an angle θ in a right triangle:
Ratio Full Name Formula Reciprocal of
sinθ Sine P/H cosecθ
cosθ Cosine B/H secθ
tanθ Tangent P/B cotθ
cosecθ Cosecant H/P sinθ
secθ Secant H/B cosθ
cotθ Cotangent B/P tanθ
■ Memory Trick (SOH-CAH-TOA): Sin = Opposite/Hypotenuse | Cos = Adjacent/Hypotenuse | Tan =
Opposite/Adjacent
1.4 Relationship Between Ratios
• tanθ = sinθ / cosθ
• cotθ = cosθ / sinθ
• sinθ × cosecθ = 1 → cosecθ = 1/sinθ
• cosθ × secθ = 1 → secθ = 1/cosθ
• tanθ × cotθ = 1 → cotθ = 1/tanθ
1.5 Trigonometric Identities
These are equations that are true for all values of θ:
Identity 1: sin²θ + cos²θ = 1 (derived from Pythagoras theorem)
Identity 2: 1 + tan²θ = sec²θ
Identity 3: 1 + cot²θ = cosec²θ
■ Tip: These identities are used to prove expressions and simplify problems. Memorize all three —
they appear in nearly every board exam!
