Trigonometric Functions Formulas for Class 11 Maths Chapter 3
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- \(\sin \theta = \frac{Opposite}{Hypotenuse}\)
- \(\sec \theta = \frac{Hypotenuse}{Adjacent}\)
- \(\cos\theta = \frac{Adjacent}{Hypotenuse}\)
- \(\tan \theta =\frac{Opposite}{Adjacent}\)
- \(csc \theta = \frac{Hypotenuse}{Opposite}\)
- \(cot \theta = \frac{Adjacent}{Opposite}\)
The Reciprocal Identities are given as:
- \(cosec\theta =\frac{1}{\sin\theta }\)
- \(sec\theta =\frac{1}{\cos\theta }\)
- \(cot\theta =\frac{1}{\tan\theta }\)
- \(sin\theta =\frac{1}{csc\theta }\)
- \(cos\theta =\frac{1}{\sec\theta }\)
- \(tan\theta =\frac{1}{cot\theta }\)
Trigonometric Values of Special Angles
| Degree | sin | cos | tan | cot | sec | cosec |
| 0∘ | 0 | 1 | 0 | Not Defined | 1 | Not Defined |
| 30∘ | \[\frac{1}{2}\] | \[\frac{√3}{2}\] | \[\frac{1}{√3}\] | √3 | \[\frac{2}{√3}\] | 2 |
| 45∘ | \[\frac{1}{√2}\] | \[\frac{1}{√2}\] | 1 | 1 | √2 | √2 |
| 60∘ | \[\frac{√3}{2}\] | \[\frac{1}{2}\] | √3 | \[\frac{1}{√3}\] | 2 | \[\frac{2}{√3}\] |
| 90∘ | 1 | 0 | Not Defined |
0 | Not Defined |
1 |
Product Trigonometric formulas:
- \(\sin\: x\cdot \cos\:y=\frac{\sin(x+y)+\sin(x-y)}{2}\)
- \(\cos\: x\cdot \cos\:y=\frac{\cos(x+y)+\cos(x-y)}{2}\)
- \(\sin\: x\cdot \sin\:y=\frac{\cos(x+y)-\cos(x-y)}{2}\)
Sum to Product Trigonometric formulas:
- \(\sin\: x+\sin\: y=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}\)
- \(\sin\: x-\sin\: y=2\cos\frac{x+y}{2}\sin\frac{x-y}{2}\)
- \(\cos\: x+\cos\: y=2\cos\frac{x+y}{2}\cos\frac{x-y}{2}\)
- \(\cos\: x-\cos\: y=-2\sin\frac{x+y}{2}\sin\frac{x-y}{2}\)<
Pythagorean Trigonometric formulas
- Sin2x + Cos2x = 1
- 1 + tan2x = sec2x
- 1 + cot2x = cosec2x
Pythagorean in Radical Form Trigonometric formulas
- sinx = ∓√1–cos2x
- tanx = ∓√sec2x-1
- cosx = ∓√1–sin2x
Odd-Even Trigonometric formulas
- Sin(-x)=-sin x
- cos(-x)=-cos x
- tan(-x)=-tan x
- cot(-x)=-cot x
- sec(-x)=-sec x
- cosec(-x)=-cosec x
Ratio or Quotient Identities are given as Trigonometric formulas:
- \( Sinθ = Cosθ \times Tanθ \)
- \( Cosθ = Sinθ \times Cotθ \)
- \( Tanθ = \frac{Sinθ}{Cosθ} \)
- \( Cotθ = \frac{Cosθ}{Sinθ} \)
Periodicity Trigonometric formulas
- \(sin(x+2\pi )=sin\; x\)
- \(cos(x+2\pi )=cos\; x\)
- \(tan(x+\pi )=tan\; x\)
- \(cot(x+\pi )=cot\; x\)
Co-function Trigonometric formulas:
- \(sin(90^{\circ}-x)=cos\; x\)
- \(cos(90^{\circ}-x)=sin\; x\)
- \(tan(90^{\circ}-x)=cot\; x\)
- \(cot(90^{\circ}-x)=tan\; x\)
Sum/Difference Trigonometric formulas:
- \( \sin (x + y) = \sin(x) \cos(y) + \cos(x) \sin(y)\)
- \(\cos(x + y) = \cos(x) \cos(y) – \sin(x) \sin(y)\)
- \(\tan(x+y)=\frac{\tan\: x+\tan\: y}{1-\tan\: x\cdot \tan\: y}\)
- \(\sin(x – y) = \sin(x) \cos(y) – \cos(x) \sin(y)\)
- \(\cos(x – y) = \cos(x) \cos(y) + \sin(x) \sin(y)\)
- \(\tan(x-y)=\frac{\tan\: x – \tan\: y}{1+\tan\: x\cdot tan\: y}\)
Double Angle Trigonometric formulas:
- \(\sin(2x) = 2\sin(x).\cos(x)\)
- \(\cos(2x) = \cos^{2}(x) – \sin^{2}(x)\)
- \(\cos(2x) = 2 \cos^{2}(x) -1\)
- \(\cos(2x) = 1 – 2 \sin^{2}(x)\)
- \(\tan(2x) = \frac{[2\: \tan(x)]}{[1 -\tan^{2}(x)]}\)
Half Angle Trigonometric formulas:
- \(\sin\frac{x}{2}=\pm \sqrt{\frac{1-\cos\: x}{2}}\)
- \(\cos\frac{x}{2}=\pm \sqrt{\frac{1+\cos\: x}{2}}\)
- \(\tan(\frac{x}{2}) = \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\)
Summary Trigonometric Functions Formulas
We have listed top important formulas for Trigonometric Functions for class 11 Chapter 3 which helps support to solve questions related to chapter Trigonometric Functions. I would like to say that after remembering the Trigonometric Functions formulas you can start the questions and answers the solution of the Trigonometric Functions chapter. If you faced any problem to find a solution of Trigonometric Functions questions, please let me know through commenting or mail.
NCERT Class 11 Maths Formulas By chapters
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 15 Statistics
- Chapter 16 Probability
NCERT Solutions Class 11 Maths by Chapters
- Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability