CBSE Class 10 Maths: Introduction to Trigonometry — Notes 2026

Trigonometric Ratios

• Defined for acute angles in right-angled triangle: sin, cos, tan, cosec, sec, cot
• SOHCAHTOA: sin=O/H, cos=A/H, tan=O/A; reciprocal identities
• Values of ratios at 0°, 30°, 45°, 60°, 90°: table from NCERT — must memorise

Trigonometric Ratios of Complementary Angles

• sin θ = cos(90°−θ); tan θ = cot(90°−θ); sec θ = cosec(90°−θ)
• CBSE application: simplify sin 47° / cos 43° = sin 47° / cos (90°−47°) = sin 47° / sin 47° = 1
• Replace 90°−θ with complementary angle to simplify expressions

Trigonometric Identities

• sin²θ + cos²θ = 1; sec²θ − tan²θ = 1; cosec²θ − cot²θ = 1
• All three derived from Pythagoras theorem applied to unit circle / right triangle
• Prove identities by LHS = RHS; never cross multiply

Proving Identities — Techniques

• Convert all to sin and cos first; simplify each side independently
• Use algebraic identities: a²−b² = (a+b)(a−b); a³+b³ = (a+b)(a²−ab+b²)
• Multiply numerator and denominator by (1+cos θ), (1−sin θ) etc. as needed

Heights and Distances

• Angle of elevation: measured upward from horizontal; angle of depression: downward
• Set up right-angled triangle; apply tan for problems with height and horizontal distance
• Two-point problems: find height of tower given two angles of elevation from different distances

CBSE Standard Numerical Types

• From top of cliff 200m high, angle of depression to boat is 30°; find distance of boat from cliff
• Two poles; angles of elevation from base of each pole given; find distance between them
• Observer sees top of tower at 45° and 30° from two positions; find height of tower

CBSE Exam Tips — Trigonometry

• Draw clear, labelled diagram for every heights and distances problem
• Rationalize irrational denominators in final answer
• Complementary angle simplification is CBSE's favourite 1-mark question