Transformation formula trigonometry ratio
In trigonometry, there are eight transformation formulas mainly. These transformation formula trigonometry class 11 can convert multiplication of two trigonometric ratios into addition of trigonometric identities. These trigonometry transformation formula will help you to cancel terms from denominator and numerator. This set of transformation formulas will help to split trigonometric function or any expression into two different functions or identities.
- 2 sin x cos y = sin (x+y) + sin (x-y)
- 2 cos x cos y = cos (x+y) + cos (x-y)
- 2 sin x sin y = cos (x-y) – cos (x+y)
- 2 cos x sin y = sin (x+y)-sin (x-y)
Basic Trigonometric Function Formulas
There are six trigonometric ratios which are mainly used to find other trigonometric identities and functions in Trigonometry. These Transformation formula trigonometry class 11 basically derived by using six trigonometric functions sin theta, cos theta, sec theta, cosec theta, tan theta and cot theta.
| Angles (In Degrees) | 0° | 30° | 45° | 60° | 90° | 180° | 270° | 360° |
| Angles (In Radians) | 0° | π/6 | π/4 | π/3 | π/2 | π | 3π/2 | 2π |
| sin | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
| cos | 1 | √3/2 | 1/√2 | 1/2 | 0 | -1 | 0 | 1 |
| tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
| cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
| csc | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
| sec | 1 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | 1 |
Periodicity Trigonometric Identities (in Radians)
Transformation formula trigonometry class 11. Please follow this link of Explanation of Mathematics formula – Click
- sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
- sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
- sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A
- sin (3π/2 + A) = – cos A & cos (3π/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
- sin (2π + A) = sin A & cos (2π + A) = cos A
Co-function trigonometry Identities (in Degrees)
- sin(90°−x) = cos x
- cos(90°−x) = sin x
- tan(90°−x) = cot x
- cot(90°−x) = tan x
- sec(90°−x) = csc x
- csc(90°−x) = sec x
Sum & Difference Trigonometry Identities
Read about Transformation formula trigonometry class 11
- 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) = (tan x + tan y)/ (1−tan x •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) = (tan x–tan y)/ (1+tan x • tan y)
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