# Trigonometry Formulas: Trigonometric Ratios, Identities and Table (Complete List)

Trigonometry is a branch of Mathematics which deals with the measurement of the angles and the sides of a triangle, and of the various relationships existing between them. Trigonometry is introduced in Class 9 ICSE and in Class 10 CBSE. To excel in Trigonometry sums it is important to understand all the Trigonometry formulas related to Trigonometric Ratios, their various relations, Trigonometric Identities and also the Trigonometric Table.

The Brainbox Tutorials provides you with the complete list of all the formulas and identities of Trigonometry useful for classes 9 and 10. You can also download the beautiful HD quality PDF in which all the formulas have been listed comprehensively.

## Basic terminology of Trigonometry

Let us understand some basic terminology of Trigonometry to understand the formulas.

## Trigonometric Ratios/ T-Ratios/ Trigonometric Functions

There are six Trigonometric ratios ( T-Ratios)- sine, cosine, tangent, cosecant, secant and cotangent. Let us consider a triangle ABC right-angled at A. Let AB be its perpendicular (p), AC be its base (b) and BC be its hypotenuse, then

 sine of angle 𝛳 = sin 𝛳 = perpendicular/hypotenuse = AB/BC cosine of angle 𝛳 = cos 𝛳 = base/hypotenuse = AC/BC tangent of angle 𝛳 = tan 𝛳 = perpendicular/base = AB/AC cosecant of angle 𝛳 = cosec 𝛳 = hypotenuse/perpendicular = BC/AB secant of angle 𝛳 = sec 𝛳 = hypotenuse/base = BC/AC cotangent of angle 𝛳 = cot 𝛳 = base/perpendicular = AC/AB

### Reciprocal Relations between Trigonometric Ratios

 sin 𝛳 = 1/cosec 𝛳 cosec 𝛳 = 1/sin 𝛳 cos 𝛳 = 1/sec 𝛳 sec 𝛳 = 1/cos 𝛳 tan 𝛳 = 1/cot 𝛳 cot 𝛳 = 1/tan 𝛳

### Quotient Relations between Trigonometric Ratios

 tan 𝛳 = sin 𝛳 / cos 𝛳 cot 𝛳 = cos 𝛳 / sin 𝛳

## Trigonometric Identities

Following are the basic Trigonometric identities. Using these identities, we can express each trigonometric ratio in terms of other trigonometric ratios.

 sin²ϴ + cos²ϴ = 1 sin²ϴ = 1 – cos²ϴ cos²ϴ = 1 – sin²ϴ 1 + tan²ϴ = sec²ϴ sec²ϴ – tan²ϴ = 1 tan²ϴ = sec²ϴ – 1 1 + cot²ϴ = cosec²ϴ cosec²ϴ – cot²ϴ = 1 cot²ϴ = cosec²ϴ – 1

## Trigonometric Table: T-Ratios of 0°, 30°, 45°, 60°, 90°

Trigonometric ratios of 0°, 30°, 45°, 60°, 90° are given in the following table:

 Angle (ϴ) 0° 30° 45° 60° 90° sin ϴ 0 1/2 1/√2 √3/2 1 cos ϴ 1 √3/2 1/√2 1/2 0 tan ϴ 0 1/√3 1 √3 not defined cosec ϴ not defined √3 1 1/√3 0 sec ϴ 1 2/√3 √2 2 not defined cot ϴ not defined √3 1 1/√3 1

## Trigonometric Ratios of complementary angles

Complementary angles are the angles the sum of whose measurements is 90°. Int trigonometry, some trigonometric functions or trigonometric ratios are complementary to each other. Following is the list of Trigonometric Ratios of complementary angles.

 sin ϴ = cos (90° – ϴ ) cos ϴ = sin (90° – ϴ ) tan ϴ = cot (90° – ϴ ) cot ϴ = tan (90° – ϴ ) sec ϴ = cosec (90° – ϴ ) cosec ϴ = sec (90° – ϴ )