CBSE Class 10 Maths Revision Notes Chapter 8 Introduction to Trigonometry 2026–27
Introduction to Trigonometry studies the relationship between the sides and acute angles of a right-angled triangle.
In CBSE Class 10 Maths, Chapter 8 covers trigonometric ratios, standard values, complementary angles and identities.
Trigonometry connects the sides and angles of a right-angled triangle. In Chapter 8, students learn how ratios such as sine, cosine and tangent are formed from the perpendicular, base and hypotenuse.
Use these CBSE Class 10 Maths Revision Notes Chapter 8 to revise Introduction to Trigonometry for the 2026–27 exams. Start with triangle terms, then revise trigonometric ratios, reciprocal relations, standard angle values, complementary angles and identities.
Key Takeaways
- Right-angled triangle: Trigonometry in Class 10 is based on perpendicular, base and hypotenuse.
- Six ratios: sin, cos, tan, cosec, sec and cot are the main trigonometric ratios.
- Standard values: 0°, 30°, 45°, 60° and 90° values are required for quick solving.
- Identities: sin²θ + cos²θ = 1 is the base identity for Chapter 8 questions.
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CBSE Class 10 Maths Revision Notes Chapter 8 at a Glance
Chapter 8 introduces trigonometry through right-angled triangles. These notes keep formulas, values and identities in one place for quick revision.
| Concept | Definition | Key Term |
| Trigonometry | Study of the relation between sides and angles of a triangle | Right-angled triangle |
| Sine | Ratio of perpendicular to hypotenuse | sin θ |
| Cosine | Ratio of base to hypotenuse | cos θ |
| Tangent | Ratio of perpendicular to base | tan θ |
| Reciprocal ratios | Ratios formed as reciprocals of sin, cos and tan | cosec, sec, cot |
| Identity | Equation true for trigonometric ratios of an angle | sin²θ + cos²θ = 1 |
These CBSE Class 10 Maths Notes Chapter 8 Introduction to Trigonometry help students revise formulas before solving NCERT-based questions.
What Is Trigonometry in Class 10 Maths Chapter 8?
The word trigonometry comes from three Greek words: tri, gon and metron. These mean three, sides and measure.
In Trigonometry Notes Class 10, the chapter deals with right-angled triangles. The focus stays on acute angles and the ratios formed by their sides.
A right-angled triangle has one angle of 90°. The side opposite the right angle is called the hypotenuse.
Right-Angled Triangle Terms Used in Trigonometry
Trigonometric ratios are written with respect to an acute angle. The names of the sides change according to the angle chosen.
For an angle θ in a right-angled triangle:
| Side | Meaning |
| Hypotenuse | Longest side, opposite the right angle |
| Perpendicular | Side opposite to angle θ |
| Base | Side adjacent to angle θ |
The Pythagoras theorem is used to connect these sides.
Hypotenuse² = Perpendicular² + Base²
If any two sides are known, the third side can be found using this relation.
Trigonometric Ratios in Introduction to Trigonometry
Trigonometric ratios compare two sides of a right-angled triangle. The six ratios are sine, cosine, tangent, cosecant, secant and cotangent.
For an acute angle θ:
| Ratio | Formula |
| sin θ | Perpendicular/Hypotenuse |
| cos θ | Base/Hypotenuse |
| tan θ | Perpendicular/Base |
| cosec θ | Hypotenuse/Perpendicular |
| sec θ | Hypotenuse/Base |
| cot θ | Base/Perpendicular |
The first three ratios are sine cosine tangent. Their reciprocal ratios are cosecant secant cotangent.
Since the hypotenuse is the longest side, sin θ and cos θ lie between 0 and 1 for acute angles.
Reciprocal Relations Between Trigonometric Ratios
Reciprocal relations help students convert one trigonometric ratio into another. These are useful in simplification and identity questions.
| Relation | Meaning |
| cosec θ = 1/sin θ | Cosecant is the reciprocal of sine |
| sec θ = 1/cos θ | Secant is the reciprocal of cosine |
| cot θ = 1/tan θ | Cotangent is the reciprocal of tangent |
| tan θ = sin θ/cos θ | Tangent uses sine and cosine |
| cot θ = cos θ/sin θ | Cotangent uses cosine and sine |
These relations also help when one ratio is given and other ratios are required.
Standard Values of Trigonometric Ratios
The standard values of trigonometric ratios are used in most Chapter 8 questions. Learn the values for 0°, 30°, 45°, 60° and 90°.
| Ratio | 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 | Not defined |
| cosec θ | Not defined | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | Not defined |
| cot θ | Not defined | √3 | 1 | 1/√3 | 0 |
tan 90° and sec 90° are not defined because cos 90° = 0.
cot 0° and cosec 0° are not defined because sin 0° = 0.
Trigonometric Ratios of Complementary Angles
Two angles are complementary when their sum is 90°. Chapter 8 uses this idea to connect pairs of trigonometric ratios.
| Formula | Paired Ratio |
| sin(90° − θ) = cos θ | sine and cosine |
| cos(90° − θ) = sin θ | cosine and sine |
| tan(90° − θ) = cot θ | tangent and cotangent |
| cot(90° − θ) = tan θ | cotangent and tangent |
| sec(90° − θ) = cosec θ | secant and cosecant |
| cosec(90° − θ) = sec θ | cosecant and secant |
These formulas help convert angles greater than 45° into angles below 45°.
Example:
cot 25° = tan(90° − 25°)
cot 25° = tan 65°
So, tan 65°/cot 25° = tan 65°/tan 65° = 1
Trigonometric Identities in Class 10 Maths Chapter 8
Trigonometric identities are equations that remain true for trigonometric ratios of an angle. They help simplify expressions and prove results.
The three main identities are:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
From the first identity:
sin²θ = 1 − cos²θ
cos²θ = 1 − sin²θ
From the second identity:
tan²θ = sec²θ − 1
sec²θ − tan²θ = 1
From the third identity:
cot²θ = cosec²θ − 1
cosec²θ − cot²θ = 1
How to Use Trigonometric Ratios in Solved Questions
Solved examples help students see how formulas work in actual questions. These examples use the same basic steps: identify sides, choose the ratio, substitute values and simplify.
Example 1: Find sin θ, cos θ and tan θ
In right-angled triangle ABC, let AC = 5 cm, BC = 3 cm and AB = 4 cm. If ∠ACB = θ, find sin θ, cos θ and tan θ.
Here, for angle θ:
Perpendicular = AB = 4 cm
Base = BC = 3 cm
Hypotenuse = AC = 5 cm
sin θ = Perpendicular/Hypotenuse = 4/5
cos θ = Base/Hypotenuse = 3/5
tan θ = Perpendicular/Base = 4/3
Example 2: Find A and B using standard values
If tan(A + B) = √3 and tan(A − B) = 1/√3, find A and B.
Given:
tan(A + B) = √3
From the standard value table:
tan 60° = √3
So, A + B = 60° …(1)
Also:
tan(A − B) = 1/√3
tan 30° = 1/√3
So, A − B = 30° …(2)
Add (1) and (2):
A + B + A − B = 60° + 30°
2A = 90°
A = 45°
Put A = 45° in A + B = 60°:
45° + B = 60°
B = 15°
So, A = 45° and B = 15°.
Example 3: Prove a trigonometric identity
Prove that sec θ(1 − sin θ)(sec θ + tan θ) = 1.
LHS = sec θ(1 − sin θ)(sec θ + tan θ)
sec θ = 1/cos θ
tan θ = sin θ/cos θ
LHS = (1/cos θ)(1 − sin θ)(1/cos θ + sin θ/cos θ)
LHS = (1/cos θ)(1 − sin θ)((1 + sin θ)/cos θ)
LHS = (1 − sin θ)(1 + sin θ)/cos²θ
LHS = (1 − sin²θ)/cos²θ
Since 1 − sin²θ = cos²θ,
LHS = cos²θ/cos²θ
LHS = 1
So, sec θ(1 − sin θ)(sec θ + tan θ) = 1.
Formula Table for Class 10 Mathematics Revision Notes Chapter 8
Students can use this table for quick revision before solving Chapter 8 questions.
| Concept | Formula |
| Pythagoras theorem | Hypotenuse² = Perpendicular² + Base² |
| Sine | sin θ = Perpendicular/Hypotenuse |
| Cosine | cos θ = Base/Hypotenuse |
| Tangent | tan θ = Perpendicular/Base |
| Cosecant | cosec θ = Hypotenuse/Perpendicular |
| Secant | sec θ = Hypotenuse/Base |
| Cotangent | cot θ = Base/Perpendicular |
| Tangent relation | tan θ = sin θ/cos θ |
| Cotangent relation | cot θ = cos θ/sin θ |
| First identity | sin²θ + cos²θ = 1 |
| Second identity | 1 + tan²θ = sec²θ |
| Third identity | 1 + cot²θ = cosec²θ |
These Class 10 Mathematics Revision Notes Chapter 8 cover the formulas needed for ratio-based and identity-based questions.
Chapter 8 Introduction to Trigonometry Summary
Class 10 Maths Chapter 8 Revision Notes begin with the right-angled triangle. The hypotenuse, perpendicular and base form all trigonometric ratios.
The six trigonometric ratios are sin θ, cos θ, tan θ, cosec θ, sec θ and cot θ. Their values depend on the angle, not on the size of the triangle.
Standard values for 0°, 30°, 45°, 60° and 90° are important for direct calculation. Complementary angle formulas connect ratios of angles whose sum is 90°.
The main trigonometric identities help simplify expressions and prove results. These CBSE Notes Class 10 Maths Chapter 8 Introduction To Trigonometry bring the main definitions, formulas and examples into a quick revision format.
Useful Important Questions Class 10 Maths Links
| Resource | Link |
| CBSE Class 10 Maths Syllabus | CBSE Class 10 Maths Syllabus |
| CBSE Class 10 Maths Revision Notes | CBSE Class 10 Maths Revision Notes |
| CBSE Extra Questions for Class 10 Maths | CBSE Extra Questions for Class 10 Maths |
| CBSE Sample Papers for Class 10 Maths | CBSE Sample Papers for Class 10 Maths |
| CBSE Class 10 Maths Formula | CBSE Class 10 Maths Formula |
| NCERT Solutions for Class 10 Maths | NCERT Solutions for Class 10 Maths |
FAQs (Frequently Asked Questions)
The six trigonometric ratios are sin, cos, tan, cosec, sec and cot. They are formed by comparing two sides of a right-angled triangle with respect to an acute angle.
sin θ = Perpendicular/Hypotenuse, cos θ = Base/Hypotenuse and tan θ = Perpendicular/Base. These three ratios are the main ratios used in Introduction to Trigonometry.
The values of 0°, 30°, 45°, 60° and 90° are most important. These values are used in direct calculations, simplification and many NCERT-based questions.
The three main identities are sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. They are used to prove and simplify trigonometric expressions.
tan 90° is not defined because tan θ = sin θ/cos θ. At 90°, cos 90° = 0, and division by zero is not defined.