Concept Topic GuideCBSE & ICSEClass 10MathematicsIntroduction to TrigonometryVerified Faculty Notes & Solutions
Introduction to Trigonometry – Class 10 Maths Chapter 8: Ratios & Identities
Class 10 Trigonometry notes: sin cos tan ratios, standard angle values, trigonometric identities, complementary angles for CBSE & ICSE.
7 students readUpdated 4 September 2026
Chapter 8: Introduction to Trigonometry
8.1 Trigonometric Ratios
In a right-angled triangle with an acute angle θ:
sin θ = Opposite / Hypotenuse (P/H)
cos θ = Adjacent / Hypotenuse (B/H)
tan θ = Opposite / Adjacent (P/B)
cosec θ = 1/sin θ = H/P
sec θ = 1/cos θ = H/B
cot θ = 1/tan θ = B/P
Also: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ
cos θ = Adjacent / Hypotenuse (B/H)
tan θ = Opposite / Adjacent (P/B)
cosec θ = 1/sin θ = H/P
sec θ = 1/cos θ = H/B
cot θ = 1/tan θ = B/P
Also: tan θ = sin θ / cos θ and cot θ = cos θ / sin θ
8.2 Values of Trigonometric Ratios for Standard Angles
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
| cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | ∞ |
| cot θ | ∞ | √3 | 1 | 1/√3 | 0 |
Memory Trick for sin values: Write 0, 1, 2, 3, 4 under 0°, 30°, 45°, 60°, 90°. Divide each by 4 and take the square root:
sin 0° = √(0/4) = 0, sin 30° = √(1/4) = 1/2, sin 45° = √(2/4) = 1/√2, sin 60° = √(3/4) = √3/2, sin 90° = √(4/4) = 1
For cos, reverse the order: cos 0° = 1, cos 30° = √3/2, etc.
sin 0° = √(0/4) = 0, sin 30° = √(1/4) = 1/2, sin 45° = √(2/4) = 1/√2, sin 60° = √(3/4) = √3/2, sin 90° = √(4/4) = 1
For cos, reverse the order: cos 0° = 1, cos 30° = √3/2, etc.
8.3 Complementary Angles
Two angles are complementary if their sum is 90°. The trigonometric ratios of complementary angles are related:
sin(90° − θ) = cos θ cos(90° − θ) = sin θ
tan(90° − θ) = cot θ cot(90° − θ) = tan θ
sec(90° − θ) = cosec θ cosec(90° − θ) = sec θ
tan(90° − θ) = cot θ cot(90° − θ) = tan θ
sec(90° − θ) = cosec θ cosec(90° − θ) = sec θ
8.4 Trigonometric Identities
Identity 1: sin²θ + cos²θ = 1
Identity 2: 1 + tan²θ = sec²θ
Identity 3: 1 + cot²θ = cosec²θ
Identity 2: 1 + tan²θ = sec²θ
Identity 3: 1 + cot²θ = cosec²θ
These identities hold for all values of θ where the ratios are defined, and are extremely useful for simplifying and proving trigonometric expressions in board exams.
Indexed Topics & Examination Keywords
#trigonometry class 10#sin cos tan#trigonometric ratios#trigonometric identities#complementary angles#NCERT maths#CBSE#ICSE#standard angles
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