3. Trigonometric Functions

Trigonometric Functions Class 11 Maths

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Complete Syllabus of Class 11 Maths Chapter 3 Trigonometric Functions:

NCERT Exercise 3.1

NCERT Exercise 3.2

NCERT Exercise 3.3

NCERT Exercise 3.4

NCERT Supplementary Exercise 3.5

NCERT Miscellaneous Exercise

NCERT Chapter 3 Examples

We have developed detailed study materials for Class 11 Maths. It covers all the basic to advance concepts, each and every NCERT solutions and important examples from the boards point of view.

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Type – I
\sin \theta =\frac{1}{{\rm cosec}\, \theta }

{\rm cosec\; }\theta =\frac{1}{\sin \theta }

\cos \theta =\frac{1}{\sec \theta }

\sec \theta =\frac{1}{\cos \theta }

\tan \theta =\frac{1}{\cot \theta } =\frac{\sin \theta }{\cos \theta }

\cot \theta =\frac{1}{\tan \theta } =\frac{\cos \theta }{\sin \theta }

Type – II

1=\sin ^{2} \theta +\cos ^{2} \theta

1-\sin ^{2} \theta =\cos ^{2} \theta

1-\cos ^{2} \theta =\sin ^{2} \theta

{\rm cosec}^{2} \theta =1+\cot ^{2} \theta

{\rm cosec}^{2} \theta -\cot ^{2} \theta =1

{\rm cosec}^{2} \theta -1=\cot ^{2} \theta

\sec ^{2} \theta =1+\tan ^{2} \theta

\sec ^{2} \theta -\tan ^{2} \theta =1

\sec ^{2} \theta -1=\tan ^{2} \theta

Type – III

\sin (A+B)=\sin A\cos B+\cos A\sin B

\cos (A+B)=\cos A\cos B-\sin A\sin B

\cos (A-B)=\cos A\cos B+\sin A\sin B

\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}

\tan (A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}

\cot (A+B)=\frac{\cot A\cot B-1}{\cot B+\cot A}

\cot (A-B)=\frac{\cot A\cot B+1}{\cot B-\cot A}

Type – IV

\sin (A+B)+\sin (A-B)=2\sin A\cos B

\sin (A+B)-\sin (A-B)=2\cos A\sin B

\cos (A+B)+\cos (A-B)=2\cos A\cos B

\cos (A+B)-\cos (A-B)=-2\sin A\sin B

Type – V

\sin 3\, \theta \, =3\sin \theta -4\sin ^{3} \theta

\cos 3\, \theta =4\cos ^{3} \theta -3\cos \theta

\tan 3\, \theta =\frac{3\tan \theta -\tan ^{3} \theta }{1-3\tan ^{2} \theta }

Type – VI

1-\cos \theta =2\sin ^{2} \frac{\theta }{2}

1+\cos \theta =2\cos ^{2} \frac{\theta }{2}

\tan \frac{\theta }{2} \, \, =\, \, \sqrt{\frac{1-\cos \theta }{1+\cos \theta } }

\frac{1-\tan \theta }{1+\tan \theta } =\tan \left(\frac{\pi }{4} -\theta \right)

\frac{1+\tan \theta }{1-\tan \theta } =\tan \left(\frac{\pi }{4} +\theta \right)

1 + sin\theta = \left ( \cos \frac{\theta}{2} + \sin \frac{\theta}{2} \right ) ^2

1 – sin\theta = \left ( \cos \frac{\theta}{2} – \sin \frac{\theta}{2} \right ) ^2

Type – VII

\sin A+\sin B=2\sin \left(\frac{A+B}{2} \right)\, \, \cos \left(\frac{A-B}{2} \right)

\sin A-\sin B=2\cos \left(\frac{A+B}{2} \right)\, \, \sin \left(\frac{A-B}{2} \right)

\cos A+\cos B=2\cos \left(\frac{A+B}{2} \right)\, \, \cos \left(\frac{A-B}{2} \right)

\cos A-\cos B=-2\sin \left(\frac{A+B}{2} \right)\, \, \sin \left(\frac{A-B}{2} \right)

Type – VIII

\sin 2\, \theta =2\sin \theta \cos \theta =\frac{2\tan \theta }{1+\tan ^{2} \theta }

\cos 2\, \theta =\cos ^{2} \theta -\sin ^{2} \theta \, =2\cos ^{2} \theta -1\, =1-2\sin ^{2} \theta \, =\frac{1-\tan ^{2} \theta }{1+\tan ^{2} \theta }

\tan 2\, \theta =\frac{2\tan \theta }{1-\tan ^{2} \theta }

Lectures for Trigonometric Functions Class 11 Maths

Lecture - 1

  • Meaning and origin of Word Trigonometry
  • Basics of Angles: Positive angles, negative angles, vertex with animations
  • Measuring an angle
  • Basics of Degree measure, minutes and seconds
  • Basics of Radian measure with animation
  • Relation between degree measure and radian measure
  • NCERT Exercise 3.1 Question 1 (Degree to radian conversion)
  • NCERT Miscellaneous Exercise (Q11 & Q9)

Hindi + English

Lecture - 2

  • Radian to degree conversion
  • NCERT Exercise 3.1 (Q2 to Q7)
  • Radian measure for non-unit circles

Hindi + English

Lecture - 3

  • Basics of unit circle in trigonometry
  • Signs of trigonometry ratios in different quadrants and at different angles
  • Shortcut trick to remember signs of trigonometry ratios in different quadrant
  • NCERT Exercise 3.2 (Q1 to Q5)
  • Relationship between trigonometric ratios of positive and negative angles

Hindi + English

Lecture - 4

  • Working with unit circle in trigonometry through horizontal line, coterminal angles and allied angles
  • NCERT Exercise 3.2 (Q6 to Q10)

Hindi + English

Lecture - 5

  • Working with unit circle in trigonometry through vertical line
  • Some extra questions from NCERT Exemplar problem, CBSE Support material and other books explaining working with coterminal and allied angles
  • Working with unit circle in trigonometry (on horizontal and vertical line)
  • NCERT Example 9
  • NCERT Exercise 3.3 (Q1 & Q3)

Hindi + English

Lecture - 6

  • NCERT Exercise 3.3 (Q2 to Q4)
  • Derivation of identity for sin(A+B) using example of sin75°
  • Value of sin75° using sin(A+B) identity NCERT Exercise 3.3 Question 5 (i)
  • Derivation for sin(A-B)
  • Derivation for cos(A+B)
  • Derivation for cos(A-B)
  • Derivation for tan(A+B) and tan(A-B)
  • NCERT Exercise 3.3 Question 5 (ii) Value of tan15°
  • NCERT Example 13

Hindi + English

Lecture - 7

  • NCERT Exercise 3.3 (Q6 to Q11)
  • Derivation for sin(A+B)+sin(A-B), sin(A+B)-sin(A-B), cos(A+B)+cos(A-B), cos(A+B)-cos(A-B)
  • Derivation for twice angles sin2x, cos2x and tan2x
  • NCERT Exercise 3.3 (Q23 & Q24)

Hindi + English

Lecture - 8

  • Derivation for thrice angles sin3x, cos3x and tan3x
  • Derivation for sinA+sinB, sinA-sinB, cosA+cosB and cosA-cosB
  • NCERT Exercise 3.3 (Q12 to Q15)

Hindi + English

Lecture - 9

  • NCERT Exercise 3.3 (Q16 to Q22)
  • NCERT Exercise 3.3 Question 25
  • Derivation for cot(A+B) and cot(A-B)
  • NCERT Example 14

Hindi + English

Lecture - 10

  • Miscellaneous Exercise (Q1 to Q7)
  • NCERT Example 25 and 26

Hindi + English

Lecture - 11

  • Derivation for half angles, sin(x/2), cos(x/2) and tan(x/2)
  • NCERT Example 27 to 29
  • Miscellaneous Exercise (Q8 to Q10)

Hindi + English

Lecture - 12

  • Introduction to Trigonometry Equations
  • Derivation of general solutions for zeroes trigonometry equations
  • Derivation of general solutions for non zeroes trigonometry equations
  • General Solutions and Principal Solutions
  • NCERT Exercise 3.4 (Q1 to Q9)
  • NCERT Example 22 & 24

Hindi + English

Lecture - 13

  • Purpose for Law of Sines and Law of cosines
  • Derivation of Law of sines for Acute angles
  • Derivation of Law of sines for Obtuse angles
  • Derivation of Law of cosines for Acute angles
  • Derivation of Law of cosines for Obtuse angles
  • Derivation of Law of sines and Law of cosines for right angle

Hindi + English

Formula Sheet for Quick Reference (Both Class 11 & 12)

Inverse Trigonometry Formula Sheet 1
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Inverse Trigonometry Formula Sheet 2
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Class 11 All Trigonometry Formulas Mobile
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