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CBSE Class 11 — Notes, Chapters & Practice Quizzes

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Mathematics · 14 chapters
Summary, key terms, extra questions with answers and a practice quiz with AI diagnosis for each.

Chapter 3: Trigonometric FunctionsClass 11 Mathematics — summary, notes, extra questions & MCQ quiz

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The relation between radian and degree measure is:

Summary

Trigonometric ratios of acute angles are generalised here to trigonometric functions of any angle. Angles are measured in degrees or in radians, related by \(\pi\text{ radian}=180^\circ\), and an arc of length \(l\) in a circle of radius \(r\) subtends \(\theta=l/r\) so \(l=r\theta\). Using a unit circle, \(\cos x\) and \(\sin x\) are the coordinates of a point, giving \(\sin^2 x+\cos^2 x=1\), \(1+\tan^2 x=\sec^2 x\) and \(1+\cot^2 x=\operatorname{cosec}^2 x\). Sine and cosine are periodic with period \(2\pi\); their signs vary by quadrant. The chapter derives the sum and difference formulas, e.g. \(\cos(x+y)=\cos x\cos y-\sin x\sin y\) and \(\sin(x+y)=\sin x\cos y+\cos x\sin y\), the double- and triple-angle identities such as \(\sin 2x=2\sin x\cos x\) and \(\cos 2x=1-2\sin^2 x\), and the product-to-sum and sum-to-product transformations. These identities let us evaluate functions at angles like \(15^\circ\) and prove a wide range of trigonometric equalities.

Angles: degree and radian measureArc length \(l=r\theta\)Trigonometric functions on the unit circleSigns, domain and range by quadrantSum and difference identitiesDouble, triple and half-angle formulaeProduct-to-sum and sum-to-product formulae

Key terms

Radian measure
Angle subtended at the centre by an arc equal to the radius; \(\pi\text{ rad}=180^\circ\).
Arc length relation
In a circle of radius \(r\), \(l=r\theta\) where \(\theta\) is in radians.
Pythagorean identity
\(\sin^2 x+\cos^2 x=1\), with \(1+\tan^2 x=\sec^2 x\) and \(1+\cot^2 x=\operatorname{cosec}^2 x\).
Sum formula
\(\cos(x+y)=\cos x\cos y-\sin x\sin y\); \(\sin(x+y)=\sin x\cos y+\cos x\sin y\).
Double angle
\(\sin 2x=2\sin x\cos x\); \(\cos 2x=\cos^2 x-\sin^2 x=1-2\sin^2 x\).
Periodicity
\(\sin\) and \(\cos\) repeat every \(2\pi\); \(\tan\) and \(\cot\) repeat every \(\pi\).

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Radian measure
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Angle subtended at the centre by an arc equal to the radius; \(\pi\text{ rad}=180^\circ\).
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Practice quiz · Trigonometric Functions

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Trigonometric Functions

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