CBSE · Class 10
Trigonometry Formulas — Class 10
All trigonometric ratios, identities, complementary angle formulas and standard values for CBSE Class 10 Maths Chapter 8 & 9.
For reference only. Always verify formulas and information against your official NCERT textbooks or board-prescribed materials before use in exams. Learnizo does not guarantee absolute accuracy.
Ch 1.Trigonometric Ratios
| Formula / Relation | Expression |
|---|---|
| sin θ | sin θ = Opposite / Hypotenuse = P/H |
| cos θ | cos θ = Adjacent / Hypotenuse = B/H |
| tan θ | tan θ = Opposite / Adjacent = P/B = sin θ / cos θ |
| cosec θ | cosec θ = 1/sin θ = H/P |
| sec θ | sec θ = 1/cos θ = H/B |
| cot θ | cot θ = 1/tan θ = B/P = cos θ / sin θ |
Ch 2.Standard Values Table
| Formula / Relation | Expression |
|---|---|
| sin 0° | sin 0° = 0 |
| sin 30° | sin 30° = 1/2 |
| sin 45° | sin 45° = 1/√2 = √2/2 ≈ 0.707 |
| sin 60° | sin 60° = √3/2 ≈ 0.866 |
| sin 90° | sin 90° = 1 |
| cos 0° | cos 0° = 1 |
| cos 30° | cos 30° = √3/2 |
| cos 45° | cos 45° = 1/√2 |
| cos 60° | cos 60° = 1/2 |
| cos 90° | cos 90° = 0 |
| tan 0° | tan 0° = 0 |
| tan 30° | tan 30° = 1/√3 = √3/3 ≈ 0.577 |
| tan 45° | tan 45° = 1 |
| tan 60° | tan 60° = √3 ≈ 1.732 |
| tan 90° | tan 90° = undefined (∞) |
Ch 3.Pythagorean Identities
| Formula / Relation | Expression |
|---|---|
| Identity 1 | sin²θ + cos²θ = 1 |
| Identity 2 | 1 + tan²θ = sec²θ |
| Identity 3 | 1 + cot²θ = cosec²θ |
Ch 4.Complementary Angle Formulas
| Formula / Relation | Expression |
|---|---|
| sin & cos complement | sin(90° − θ) = cos θ |
| cos & sin complement | cos(90° − θ) = sin θ |
| tan & cot complement | tan(90° − θ) = cot θ |
| cot & tan complement | cot(90° − θ) = tan θ |
| sec & cosec complement | sec(90° − θ) = cosec θ |
| cosec & sec complement | cosec(90° − θ) = sec θ |
Ch 5.Useful Relationships
| Formula / Relation | Expression |
|---|---|
| tan in terms of sin & cos | tan θ = sin θ / cos θ |
| sin²θ + cos²θ | sin²θ + cos²θ = 1 (always) |
| sin θ × cosec θ | sin θ × cosec θ = 1 |
| cos θ × sec θ | cos θ × sec θ = 1 |
| tan θ × cot θ | tan θ × cot θ = 1 |
Frequently Asked Questions
What is the easiest way to remember trigonometric values?
Use the 0, 1, 2, 3, 4 rule for sin: sin 0° = √0/2 = 0, sin 30° = √1/2 = 1/2, sin 45° = √2/2 = 1/√2, sin 60° = √3/2, sin 90° = √4/2 = 1. For cos, the values go in reverse order. For tan, divide the corresponding sin and cos values.
How many Pythagorean identities are there in Class 10?
There are 3 Pythagorean identities: (1) sin²θ + cos²θ = 1, (2) 1 + tan²θ = sec²θ, (3) 1 + cot²θ = cosec²θ. All three are derived from the fundamental right-angle triangle relationship a² + b² = c². Master these three and their rearrangements — they appear in almost every trigonometry proof question.
What is the difference between trigonometry in Class 10 and Class 11?
Class 10 trigonometry is restricted to acute angles (0° to 90°) in a right-angled triangle. Class 11 extends to all angles (0° to 360° and beyond) using the unit circle, adding formulas for sin(A+B), sin(A−B), 2A, etc. Class 10 identities and standard values are the foundation for Class 11 — mastering them completely is essential.
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