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Bihar Board Class 10 · Maths · Matric exam 2027

Chapter 8: Introduction to Trigonometry — notes

The chapter’s 6 parts in the book’s order — the first idea of each and the points Medha Ma’am writes on the board — and the summary at the end. The full lesson and a check question for each part are in the app.

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  1. 1. Why we study trigonometry

    Okay, so imagine you're visiting the Qutub Minar.

    • • Trigonometry = study of relation between sides and angles of a triangle
    • • 'tri' = three, 'gon' = sides, 'metron' = measure
    • • Used by early astronomers to find distances of stars and planets
    • • We study trigonometric ratios of acute angles of a right triangle

  2. 2. The six trigonometric ratios

    Okay, so look at this right triangle ABC, with angle A an acute angle.

    • • sin A = opposite/hypotenuse = BC/AC
    • • cos A = adjacent/hypotenuse = AB/AC
    • • tan A = opposite/adjacent = BC/AB
    • • cosec A = 1/sin A, sec A = 1/cos A, cot A = 1/tan A
    • • tan A = sin A/cos A, cot A = cos A/sin A
    • • Ratios same for same angle, whatever the triangle's size

  3. 3. Finding ratios from one given ratio

    Okay, so — suppose you're told just one trigonometric ratio of an angle.

    • • Given tan A = 4/3 so BC = 4k, AB = 3k
    • • AC² = AB² + BC² = 25k² so AC = 5k
    • • sin A = BC/AC = 4/5
    • • cos A = AB/AC = 3/5
    • • cot A = 3/4, cosec A = 5/4, sec A = 5/3

  4. 4. Trigonometric ratios of specific angles 0°, 30°, 45°, 60°, 90°

    Okay, so now let's find the ratios for some special angles — 0°, 30°, 45°, 60°, and 90°.

    • • sin 45° = 1/√2, cos 45° = 1/√2, tan 45° = 1
    • • sin 30° = 1/2, cos 30° = √3/2, tan 30° = 1/√3
    • • sin 60° = √3/2, cos 60° = 1/2, tan 60° = √3
    • • sin 0° = 0, cos 0° = 1
    • • sin 90° = 1, cos 90° = 0
    • • tan 90° and cot 0° not defined

  5. 5. Trigonometric ratios of complementary angles

    Okay, so — two angles are complementary if they add up to 90°.

    • • A and C complementary: A + C = 90°
    • • sin (90°−A) = cos A
    • • cos (90°−A) = sin A
    • • tan (90°−A) = cot A, cot (90°−A) = tan A
    • • sec (90°−A) = cosec A, cosec (90°−A) = sec A
    • • Example: tan 65°/cot 25° = tan 65°/tan 65° = 1

  6. 6. Trigonometric identities

    Okay, so — what's an identity?

    • • AB² + BC² = AC² (Pythagoras)
    • • Divide by AC²: cos²A + sin²A = 1
    • • Divide by AB²: 1 + tan²A = sec²A
    • • Divide by BC²: cot²A + 1 = cosec²A
    • • Example: tan A = 1/√3 gives sec²A = 4/3, sec A = 2/√3

Summary

Okay, so let's look back at everything we've done in this chapter. We started with a simple picture, someone looking up at the Qutub Minar, and that gave us a right triangle. From there, trigonometry became the study of how the sides and angles of a triangle relate to each other. Then we met the six ratios of an acute angle, sin, cos, tan, cosec, sec, cot. Remember, these come from the opposite side, the adjacent side, and the hypotenuse. And here's the nice part — these ratios don't change, no matter how big or small the triangle is. After that, you learned something useful. If just one ratio is given, you can find all the other five, using the Pythagoras theorem. Then we worked out exact values of these ratios for 0°, 30°, 45°, 60°, and 90°. You also saw a lovely connection between complementary angles — so sin(90° − A) = cos A, and other pairs just like it. And finally, we proved three identities that hold for every angle where the ratios make sense, cos²A + sin²A = 1, 1 + tan²A = sec²A, and cot²A + 1 = cosec²A. Now, thinking back over all of this — which of these ideas did you find the most interesting?

AskMedha · Medha Ma’am — Bihar Board Class 10 Maths, Chapter 8. Written from the textbook, checked twice.

Questions parents and students ask

How do I get the "Introduction to Trigonometry" notes as a PDF?
Press "Save as PDF" — the phone’s print sheet opens; choose "Save as PDF" there. The PDF holds the notes only.
Where are these notes written from?
From the chapter’s own textbook text, part by part, in the book’s own terms; a second, independent model then checked every part against the book. The full lesson, a check question for each part and the practice are in the AskMedha app.

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