Class 10 Maths — Chapter 8: TRIGONOMETRY
Chapter 8: TRIGONOMETRY is a chapter in Class 10 Maths (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 6 topics including Identifying Sides Relative to an Acute Angle, The Six Trigonometric Ratios, Reciprocal Identities. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Identifying Sides Relative to an Acute AngleCore concepthypotenuseopposite sideadjacent sideacute angleright triangle
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▸The Six Trigonometric RatiosCore conceptsinecosinetangentratioSOH CAH TOA
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▸Reciprocal IdentitiesCore conceptreciprocalcosecantsecantcotangentidentity
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▸Quotient IdentitiesCore conceptquotienttangentcotangentsin/cosidentity
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▸Invariance of Trigonometric Ratiossimilar trianglesangle measureconstant ratioproportional sidesinvariance
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▸Calculating All Ratios from One Given RatioCore conceptPythagorean theoremfind all ratiosgiven ratiocalculateproblem solving
Chapter Summary
Correctly identifying the hypotenuse, the side opposite to a given acute angle, and the side adjacent to that angle in a right-angled triangle. This is the foundational skill for defining trigonometric ratios.
Defining the six trigonometric ratios—sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot)—as ratios of the lengths of the sides of a right triangle.
Understanding and applying the reciprocal relationships between trigonometric ratios: cosec A is the reciprocal of sin A, sec A is the reciprocal of cos A, and cot A is the reciprocal of tan A.
Understanding and using the relationships tan A = sin A / cos A and cot A = cos A / sin A to express tangent and cotangent in terms of sine and cosine.
Understanding the concept that the value of a trigonometric ratio depends only on the measure of the angle, not on the lengths of the sides of the triangle, as demonstrated by using similar triangles.
Using one known trigonometric ratio to construct a right triangle, finding the length of the third side using the Pythagorean theorem, and then calculating the values of the other five trigonometric ratios.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Explain trigonometry simply. Get Solution →
- Show real-world angle uses. Get Solution →
- Calculate a right triangle's side. Get Solution →
- What does the Greek word 'tri' mean, as used in the word 'trigonometry'? Get Solution →
- In a right triangle ABC, how is the 'sine of ∠A' defined? Get Solution →
- Which trigonometric ratio is the reciprocal of cos A? Get Solution →
- According to the text, tan A is equal to which of the following ratios? Get Solution →
- Who was the first person mentioned in the text to use the abbreviated notation 'sin'? Get Solution →
Did you know?
- 💡 The ancient Egyptians used early trigonometry to build the massive pyramids.
- 💡 Your phone's GPS uses trigonometry to figure out your exact location.
- 💡 Music and sound waves are often modeled using trigonometric functions.
- 💡 Triangles are the only rigid polygon, making them super strong in buildings.
- 💡 Sailors navigate by calculating angles to stars using trigonometry.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 6 key topics: Identifying Sides Relative to an Acute Angle, The Six Trigonometric Ratios, Reciprocal Identities, Quotient Identities, Invariance of Trigonometric Ratios, and more. The BrainWeave AI tutor explains each one with examples.
Is Chapter 8: TRIGONOMETRY important for board exams?
Yes — Class 10 is a CBSE board exam year, and every NCERT chapter is part of the syllabus. Use BrainWeave's AI tutor to master this chapter, then practice with the auto-generated quizzes and mind maps.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 10?
Yes. BrainWeave's free Spark plan gives generous daily messages — enough for regular homework. Premium features unlock when you bring your own free Google Gemini API key.
Can I use voice chat for this chapter?
Absolutely. Tap the mic, ask any question about Chapter 8: TRIGONOMETRY, and the AI tutor will explain it back in voice and text.
How is BrainWeave better than static NCERT solutions sites?
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