Chapter Hub
Introduction to Trigonometry
Introduction to trigonometry begins with the six ratios formed from the sides of a right triangle. The chapter trains you to connect angle, side, and ratio in a clean and exam-ready way. For CBSE Class 10, this chapter is important because it supports direct questions, identity-based simplification, value tables, and application questions based on triangles and heights.
Difficulty
Medium
Study time
96-120 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 96 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
Start with one of the buckets below, then open the full map when you want the complete concept roadmap.
Basic Trigonometric Ratios
Covers Trigonometric ratios, Sin A, cos A and tan A and Cosec A, sec A and cot A.
Open mapRelations and Identities
Covers Trig ratios for complementary angles, Identity sin^2 A + cos^2 A = 1, Identity 1 + tan^2 A = sec^2 A and Identity 1 + cot^2 A = cosec^2 A.
Open mapStandard Values
Covers Values at 0, 30, 45, 60 and 90 degrees and Error detection in standard values.
Open mapApplications and Reading Diagrams
Covers Choosing correct ratio from a situation, Ratio interpretation from diagram and Using trig identities to simplify expressions.
Open mapKey Concepts
Concepts grouped the way the chapter is taught — open the group that matches what you want to revise.
Basic Trigonometric Ratios
Covers Trigonometric ratios, Sin A, cos A and tan A and Cosec A, sec A and cot A.
Trigonometric ratios
Trigonometric ratios are the fixed ratios between the sides of a right triangle for a chosen acute angle.
Sin A, cos A and tan A
Sin A, cos A, and tan A are the basic trigonometric ratios formed from the opposite, adjacent, and hypotenuse sides of a right triangle.
Cosec A, sec A and cot A
Cosec A, sec A, and cot A are the reciprocal trigonometric ratios of sine, cosine, and tangent.
Relations and Identities
Covers Trig ratios for complementary angles, Identity sin^2 A + cos^2 A = 1, Identity 1 + tan^2 A = sec^2 A and Identity 1 + cot^2 A = cosec^2 A.
Trig ratios for complementary angles
Trigonometric ratios of complementary angles are related by swapping sine with cosine, tangent with cotangent, and secant with cosecant.
Identity sin^2 A + cos^2 A = 1
The identity sin squared A plus cos squared A equals 1 is a fundamental trigonometric relation for every angle A.
Identity 1 + tan^2 A = sec^2 A
The identity 1 plus tan squared A equals sec squared A is a standard trigonometric identity used for simplification and verification.
Identity 1 + cot^2 A = cosec^2 A
The identity 1 plus cot squared A equals cosec squared A is a standard trigonometric relation used for simplification and checking answers.
Standard Values
Covers Values at 0, 30, 45, 60 and 90 degrees and Error detection in standard values.
Values at 0, 30, 45, 60 and 90 degrees
These are the standard trigonometric values of sine, cosine, tangent, cosecant, secant, and cotangent for key angles used in Class 10.
Error detection in standard values
Error detection in standard values means finding and correcting wrong entries in the standard trigonometric value table.
Applications and Reading Diagrams
Covers Choosing correct ratio from a situation, Ratio interpretation from diagram and Using trig identities to simplify expressions.
Choosing correct ratio from a situation
Choosing the correct ratio from a situation means selecting the trigonometric ratio that matches the given sides or the required unknown in a word problem.
Ratio interpretation from diagram
Ratio interpretation from a diagram means reading a right-triangle sketch correctly and deciding which trig ratio the marked sides represent.
Using trig identities to simplify expressions
Using trigonometric identities to simplify expressions means replacing one trig form with another so the expression becomes shorter or easier to solve.
Exam Intelligence
The traps that cost marks in this chapter, and how its main concepts turn up in the paper.
High Probability Topics
- Trigonometric ratios
- Sin A, cos A and tan A
- Cosec A, sec A and cot A
- Trig ratios for complementary angles
- Values at 0, 30, 45, 60 and 90 degrees
- Identity sin2 A + cos2 A = 1
- Identity 1 + tan2 A = sec2 A
- Identity 1 + cot2 A = cosec2 A
Common Traps
- Mixing up opposite and adjacent with respect to the chosen angle.
- Using the reciprocal ratio without flipping the fraction.
- Swapping the standard values of 30 degrees and 60 degrees.
- Forgetting that tan 90 degrees is not defined.
- Dropping the square in trig identities.
How CBSE Asks This Chapter
- Trigonometric ratios
CBSE may ask you to identify the correct ratio from a triangle, calculate a ratio from given sides, or choose the side pair used in a trigonometric ratio.
- Sin A, cos A and tan A
CBSE may ask for the value of a ratio from given side lengths, or ask which ratio matches a side arrangement in a triangle.
- Cosec A, sec A and cot A
CBSE may ask to convert a basic ratio into its reciprocal, or choose the correct reciprocal ratio from side lengths.
- Trig ratios for complementary angles
CBSE may ask you to write the complementary identity, or evaluate a trigonometric ratio using the complementary angle relation.
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
Remember
For a right triangle with acute angle A: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.Trap to avoid
Students often mix up opposite side and adjacent side, especially when the triangle is drawn in a different orientation.
Remember
sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent.Trap to avoid
Students often write tan A as adjacent divided by opposite, but that is actually cot A.
Remember
cosec A = 1/sin A = hypotenuse/opposite, sec A = 1/cos A = hypotenuse/adjacent, cot A = 1/tan A = adjacent/opposite.Trap to avoid
Students sometimes write sec A as adjacent over hypotenuse, but that is cosine, not secant.
Trig ratios for complementary angles
Remember
sin(90 degrees - A) = cos A, cos(90 degrees - A) = sin A, tan(90 degrees - A) = cot A, cot(90 degrees - A) = tan A, sec(90 degrees - A) = cosec A, cosec(90 degrees - A) = sec A.Trap to avoid
Students often use the same ratio on both sides of the identity instead of switching to the complementary pair.
Values at 0, 30, 45, 60 and 90 degrees
Remember
Standard values: sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1; cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0; tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 is not defined.Trap to avoid
Students sometimes interchange 30 degrees and 60 degrees values or forget that tan 90 degrees is not defined.
Identity sin^2 A + cos^2 A = 1
Remember
sin2 A + cos2 A = 1 for every angle A.Trap to avoid
Students sometimes write sin A plus cos A equals 1, but the squares are essential and cannot be removed.
Identity 1 + tan^2 A = sec^2 A
Remember
1 + tan2 A = sec2 A.Trap to avoid
Students often write 1 plus tan A equals sec A, but the squares are required on both trig terms.
Identity 1 + cot^2 A = cosec^2 A
Remember
1 + cot2 A = cosec2 A.Trap to avoid
Students sometimes write 1 plus cot A equals cosec A, but the squared form is the correct one.
Choosing correct ratio from a situation
Remember
Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent.Trap to avoid
Students often choose a ratio only because it sounds familiar, not because it matches the sides in the question.
Ratio interpretation from diagram
Remember
Opposite and adjacent are always measured with respect to the chosen acute angle; the hypotenuse is opposite the right angle and does not change.Trap to avoid
Students often label the same side as opposite for one angle and then reuse it for another angle without checking the new reference angle.
Using trig identities to simplify expressions
Remember
Use the standard identities: sin2 A + cos2 A = 1, 1 + tan2 A = sec2 A, and 1 + cot2 A = cosec2 A.Trap to avoid
Students often try to expand every term instead of spotting the matching identity first.
Error detection in standard values
Remember
Standard values must follow the correct table: sin 30 = 1/2, sin 60 = root 3/2, cos 30 = root 3/2, cos 60 = 1/2, tan 45 = 1, and tan 90 is not defined.Trap to avoid
Students often accept a wrong table entry because it looks similar to a correct one.
| Concept | Remember | Trap to avoid |
|---|---|---|
| Trigonometric ratios | For a right triangle with acute angle A: sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. | Students often mix up opposite side and adjacent side, especially when the triangle is drawn in a different orientation. |
| Sin A, cos A and tan A | sin A = opposite/hypotenuse, cos A = adjacent/hypotenuse, tan A = opposite/adjacent. | Students often write tan A as adjacent divided by opposite, but that is actually cot A. |
| Cosec A, sec A and cot A | cosec A = 1/sin A = hypotenuse/opposite, sec A = 1/cos A = hypotenuse/adjacent, cot A = 1/tan A = adjacent/opposite. | Students sometimes write sec A as adjacent over hypotenuse, but that is cosine, not secant. |
| Trig ratios for complementary angles | sin(90 degrees - A) = cos A, cos(90 degrees - A) = sin A, tan(90 degrees - A) = cot A, cot(90 degrees - A) = tan A, sec(90 degrees - A) = cosec A, cosec(90 degrees - A) = sec A. | Students often use the same ratio on both sides of the identity instead of switching to the complementary pair. |
| Values at 0, 30, 45, 60 and 90 degrees | Standard values: sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1; cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0; tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 is not defined. | Students sometimes interchange 30 degrees and 60 degrees values or forget that tan 90 degrees is not defined. |
| Identity sin^2 A + cos^2 A = 1 | sin2 A + cos2 A = 1 for every angle A. | Students sometimes write sin A plus cos A equals 1, but the squares are essential and cannot be removed. |
| Identity 1 + tan^2 A = sec^2 A | 1 + tan2 A = sec2 A. | Students often write 1 plus tan A equals sec A, but the squares are required on both trig terms. |
| Identity 1 + cot^2 A = cosec^2 A | 1 + cot2 A = cosec2 A. | Students sometimes write 1 plus cot A equals cosec A, but the squared form is the correct one. |
| Choosing correct ratio from a situation | Match the known and required sides with the angle: sine uses opposite and hypotenuse, cosine uses adjacent and hypotenuse, tangent uses opposite and adjacent. | Students often choose a ratio only because it sounds familiar, not because it matches the sides in the question. |
| Ratio interpretation from diagram | Opposite and adjacent are always measured with respect to the chosen acute angle; the hypotenuse is opposite the right angle and does not change. | Students often label the same side as opposite for one angle and then reuse it for another angle without checking the new reference angle. |
| Using trig identities to simplify expressions | Use the standard identities: sin2 A + cos2 A = 1, 1 + tan2 A = sec2 A, and 1 + cot2 A = cosec2 A. | Students often try to expand every term instead of spotting the matching identity first. |
| Error detection in standard values | Standard values must follow the correct table: sin 30 = 1/2, sin 60 = root 3/2, cos 30 = root 3/2, cos 60 = 1/2, tan 45 = 1, and tan 90 is not defined. | Students often accept a wrong table entry because it looks similar to a correct one. |
Practice
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