Trigonometry Formulas For Class 11

Trigonometry is a branch of mathematics which studies the relationships that involve angles and lengths of triangles. It is a very important topic of mathematics just like an element of statistics, linear algebra and calculus. In addition to mathematics, it also contributes majorly to engineering, physics, astronomy and architectural design. Trigonometry Formulas for class 11 plays a crucial role in solving any problem related to this chapter.

Class 11 Trigonometry Formulas List

CBSE Class 11 mathematics contains Trigonometric functions where you need to learn many formulae. This chapter lays the foundation to Inverse trigonometric functions in class 12. So, it is a very important chapter where students have to concentrate more. Trigonometric is a subject where there are formulas for everything and without which you cannot solve a problem.  Students always feel confused between these formulas. This is the reason, we at BYJU’S provide all the important formulas at a single page for easy reading and comparing. We believe, Trigonometry formulas provided here will help Class 11 students to learn them and can have a quick glance when needed.

Trigonometry Class 11 Formulas
\(\sin (-\theta ) = -\sin \theta\)
\(\cos (-\theta ) = \cos \theta\)
\(\tan (-\theta ) = -\tan \theta\)
\( cosec (-\theta ) = -cosec \theta\)
\(\sec (-\theta ) = \sec \theta\)
\(\cot (-\theta ) = -\cot \theta\)
Product to Sum Formulas
\(\sin \, x \,\ sin \, y = \frac{1}{2}\left [ \cos\left ( x – y \right ) -\cos \left ( x+y \right ) \right ]\)
\(\cos\, x \, \cos\, y = \frac{1}{2}\left [ \cos \left ( x – y \right ) + \cos \left ( x+y \right ) \right ]\)
\(\sin\, x \, \cos\, y = \frac{1}{2}\left [ \sin\left ( x + y \right ) + \sin \left ( x-y \right ) \right ]\)
\( \cos\, x \, \sin\, y = \frac{1}{2}\left [ \sin\left ( x + y \right ) – \sin\left ( x-y \right ) \right ]\)
Sum to Product Formulas
\(\sin\, x + \sin \, y = 2\, \sin \left ( \frac{x+y}{2} \right ) \cos \left ( \frac{x-y}{2} \right )\)
\(\sin\, x -\sin\, y = 2\, \cos \left ( \frac{x+y}{2} \right ) \sin \left ( \frac{x-y}{2} \right )\)
\(\cos \, x + \cos \, y = 2 \, \cos \left ( \frac{x+y}{2} \right ) \cos\left ( \frac{x-y}{2} \right )\)
\(\cos\, x -\cos\, y = – 2 \, \sin \left ( \frac{x+y}{2} \right ) \sin \left ( \frac{x-y}{2} \right )\)
Identities
sin2 A + cos2 A = 1
1+tan2 A = sec2 A
1+cot2 A = cosec2 A

Sign of Trigonometric Functions in Different Quadrants

Quadrants→ I II III IV
Sin A + +
Cos A + +
Tan A + +
Cot A  + +
Sec A + +
Cosec A  + +

Basic Trigonometric Formulas for Class 11

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

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

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

sin (A -B) = sin A cos B – cos A sin B

Based on above addition formulas for sin and cos, we get the following below formulas:

  • sin(π/2-A) = cos A
  • cos(π/2-A) = -sin A
  • sin(π-A) = sin A
  • cos(π-A) = -cos A
  • sin(π+A)=-sin A
  • cos(π+A)=-cos A
  • sin(2π-A) = -sin A
  • cos(2π-A) = cos A

If none of the angles A, B and (A ± B) is an odd multiple of π/2, then;

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

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

If none of the angles A, B and (A ± B) is a multiple of π, then;

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

Some additional formulas for sum and product of angles:

\(\cos (A + B) \cos (A – B) = \cos^{2}A – \sin^{2}B = \cos^{2}B – \sin^{2}A\)

\(\sin (A + B) \sin (A – B) = \sin^{2}A – \sin^{2}B = \cos^{2}B – \cos^{2}A\)

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

Formulas for twice of the angles:

\(\sin 2A = 2 \sin A \cos A = \frac{2\tan A}{1+\tan^{2}A}\)

\(\cos 2A = \cos^{2}A – \sin^{2}A = 1 – 2sin^{2}A = 2cos^{2}A – 1 = \frac{1-\tan^{2}A}{1 + \tan^{2}A}\)

\(\tan 2A =\frac{2 \tan A}{1 – \tan^{2}A}\)

Formulas for thrice of the angles:

\(\sin 3A = 3\sin A – 4\sin^{3}A = 4\sin(60^{\circ}-A).\sin A .\sin( 60^{\circ}+A)\)

\(\cos 3A = 4\cos^{3}A – 3\cos A = 4\cos\left ( 60^{\circ}-A \right ).\cos A . \cos\left ( 60^{\circ} +A\right )\)

\(\tan 3A = \frac{3\tan A – \tan^{3}A}{1-3\tan^{2}A} = \tan\left ( 60^{\circ}-A \right ).\tan A . \tan\left ( 60^{\circ}+A\right )\)

Also check:

Example

Example: Find the maximum value of \(\cos^{2}\cos\theta + \sin^{2} \sin\theta\) for any real value of \(\theta\)

Answer :

The maximum value of \(\cos^{2}\cos\theta = 1\) and \(\sin^{2}\sin\theta\) is \(\sin^{2} 1\) where both exist for \(\theta = \frac{\pi}{2}\). Therefore maximum value will be \(1+ \sin^{2}1\)..

10 Comments

  1. Only want useful formula of PCM

  2. thankyou so much byjus, your quick notes of formulaes helped me alot, thnx again

  3. It’s good thanks byjus

  4. Very useful notes, thanks byjus

  5. Thank you Byju’s. It is very helpful to me

  6. Thanks, guys for making our work easier and a lot more comfortable by posting all the formulas together in one place in a systematic manner

  7. Thank you Byjus. It was really helpful

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