Trigonometry Ratios | Definition, Identities, Formula & Trigonometry table |

What is Trigonometry ratios

Trigonometry comes from the Greek Word Trigonon (triangle) and metron (to measure).Trigonometry is the branch of mathematics, which describe the relationship between the sides & specific functions of the angle of the triangle.basically, trigonometry defines the ratios of side of tringle, & that ratios are expresses in the term of respective angle function. These angle functions are known as Trigonometry ratios which are expained below with thier formulas.

Trigonometric Identities, Ratio & Trigonometry values
right angle triangle

A triangle where one of its interior angles is a right angle (90 degrees).
Each side of a right triangle has a name:

Where
“a” is the perpendicular or Opposite side,

“b” is the base or Adjacent,

“h” is the hypotenuse side.

Sine, Cosine and Tangent

The three main functions in trigonometry are Sine, Cosine and Tangent.

Sine: sin(θ) = Opposite Hypotenuse
Cosine: cos(θ) = AdjacentHypotenuse
Tangent: tan(θ) = OppositeAdjacent

Where θ is the angle
When we divide Sine by Cosine we get:

sin(θ)cos(θ) = Opposite/HypotenuseAdjacent/Hypotenuse = OppositeAdjacent = tan(θ)

tan(θ) = sin(θ)cos(θ)

This is Trigonometric Identities.

Cosecant, Secant and Cotangent

Cosecant: cosec(θ) = Hypotenuse Opposite
Secant: sec(θ) = Hypotenuse Adjacent
Cotangent: cot(θ) = AdjacentOpposite

Functions

Abbreviation

Relationship

Sine Function

sin(θ)

1/ cosec(θ)

Tangent Function

tan(θ)

1/ cot(θ)

Cosine Function

cos(θ)

1/ sec(θ)

Cosecant Function

cosec(θ)

1/ sin(θ)

Secant Function

sec(θ)

1/ cos(θ)

Cotangent Function

cot(θ)

1/ tan(θ)

Trigonometry Table

Angles 30° 45° 60° 90°
Sin θ 0 ½ 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 ½ 0
Tan θ 0 1/√3 1 √3
Cosec θ 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2
Cot θ √3 1 1/√3 0

I hope, this article will help you lot to understand the Trigonometry ratios,formulas, Identities & Trigonometry table & in solving various problems related to this article, if you still have any doubts related to this article, you can ask it into the comment section. If you have any problem in any topic mathematics you can post your problem in the comment section. You will get a reply shortly.

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