Trigonometric Values

Trigonometric Values are mathematical functions that relate the angles of a right triangle to the ratios of its sides. The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan) whose values are derived using a right-angled triangle.

In this article, we are going to discuss what are trigonometric values, Definition of Trigonometric values, Trigonometric Ratio Formula, Trigonometric Value Table, and some Solved Examples based on trigonometric values.

What are Trigonometric Values?

Trigonometric values tell the relation between the ratios of sides and the angles of the right-angled triangle. There are six trigonometric values in mathematics. The six trigonometric values in mathematics are sin θ, cos θ, tan θ, cosec θ, sec θ, and cot θ. These six trigonometric values focus on the connections between a triangle’s sides and angles.

Trigonometry values refer to the study of standard angles for a given triangle to trigonometric ratios. Some of the standard values of trigonometric values for which we calculate its value are 0^o, 30^o, 45^o, 60^o, and 90^o.

Trigonometric Values Definition

Trigonometric values tells the relationship between the ratio of sides and angle of a triangle in right angled triangle. There are total of six ratios present in mathematics which are sine, cosine, tangent, cosecant, secant, cotangent.

Trigonometric Ratio Formula

The six trigonometric ratio are sin θ, cos θ, tan θ, cosec θ, sec θ and cot θ. Each ratio can be calculated by using the ratio of sides of triangles. The three given sides of right right-angled triangle are the base, perpendicular, and hypotenuse sides.

Let’s take a triangle ABC, right-angled at B. Take ∠A = θ. Now the hypotenuse of the triangle is AC, the base is AB and the perpendicular side is BC.

Formula defined for calculating all six trigonometric ratio with respect to ∠A are:

• Sin θ = Perpendicular/Hypotenuse = BC/ AC
• Cos θ = Base/Hypotenuse = AB/ AC
• Tan θ = Perpendicular/ Base = BC/AB
• Cosec θ = Hypotenuse/Perpendicular = AC/BC
• Sec θ = Hypotenuse/Base = AC/AB
• Cot θ = Base/Perpendicular = AB/BC

Also, Relation between six Trigonometric Ratios are:

• tan θ = sin θ/cos θ
• cot θ = cos θ/sin θ
• sin θ = 1/cosec θ
• cos θ = sin θ/tan θ
• cos θ = 1/sec θ
• Sec θ = tan θ/sin θ = 1/cos θ
• Cosec θ = 1/sin θ

Also, we have,

• sec θ . cos θ = 1
• cosec θ . sin θ = 1
• cot θ . tan θ = 1

Trigonometric Value Table

Values of some specific angles presented in form of table is known as Trigonometric value table. The angle can be represented both in form of radians and degree. The two different tables can be constructed on the basis of angle represented by degree and radian.

Value of trigonometric ratio can be calculated at every angle from 0^o to 360^o. The two different value table of all trigonometric ratio at some specific angles are given below:

• Trigonometric Value Table in Degree
• Trigonometric Value Table in Radian

Trigonometric Value Table in Degree

Trigonometric value table of angles in degree is represented below:

Angles in Degrees	0o	30o	45o	60o	90o
Sin	0	1/2	1/√2	√3/2	1
Cos	1	√3/2	1/√2	1/2	0
Tan	0	1/√3	1	√3	not-defined
Cosec	not-defined	2	√2	2/√3	1
Sec	1	2/√3	√2	2	not-defined
Cot	not-defined	√3/1	1	1/√3	0

Trigonometric Value Table in Radian

Trigonometric value table of angles in radians is represented below:

Angle in Radians	0c	π/6	π/4	π/3	π/2
Sin	0	1/2	1/√2	√3/2	1
Cos	1	√3/2	1/√2	1/2	0
Tan	0	1/√3	1	√3	not-defined
Cosec	not-defined	2	√2	2/√3	1
Sec	1	2/√3	√2	2	not-defined
Cot	not-defined	√3	1	1/√3	0

Read More,

• Trigonometry
• Trigonometric Formulas
• Trigonometric Identities

Examples on Trigonometric Values

Various Sexamples on Trigonometric Values are,

Example 1: If the value of Cosec θ is 3/4 , find the value of Sinθ.

Solution:

Given, Cosec θ = 3/4

We know, Sin θ = 1/Coseθ

So, Sin θ = 4/3

Example 2: Find the value tan θ if the value of Sin θ and Cos θ is 3/4 and 2/4 respectively.

Solution:

We have,

sinθ = 3/4

cosθ = 2/4

we know, tanθ = sinθ/cosθ

tanθ = (3/4)/(2/4)

tanθ = 3/2

Example 3: If the value of Sin θ is 3/5 , find the value of all other trigonometric ratios.

Solution:

Given, sin θ = 3/5

Also, sin θ = perpendicular/hypotenuse = 3/5

Now, base = √hypotenuse² – perpendicular² = √25 – 9 = √16 = 4

cos θ = base/hypotenuse = 4/5

tan θ= perpendicular/base = 3/4

cosec θ = hypotenuse/ perpendicular = 5/3

sec θ = hypotenuse/base = 5/4

cot θ = base/perpendicular = 4/3.

Practice Problems on Trigonometric Values

Some practice problems on Trigonometric Values are,

P1: If the value of Sin θ is 4/5 , find the value of all other trigonometric ratios.

P2: If the value of tan θ is 4/3 , find the value of all other trigonometric ratios.

P3: If the value of sec θ is 7/5 , find the value of cos θ.

P4: If the value of tan θ is 7/5 , find the value of cot θ.

Trigonometric Values: FAQs

What are Formulas of Trigonometric Functions?

Formulas of Trigonometric Functions are

• sin θ = perpendicular/hypotenuse
• cos θ = base/hypotenuse
• tan θ = perpendicular/base

What is Relation Between Sin θ and Cosec θ?

Sin θ = 1/Cosec θ. Cosec θ is inverse of Sin θ.

How Angle 30^o can be Represented in Radian Form?

The angle 30^o is represented as π/6 in radian form.

What is Value of Cot 0^o ?

Value of cot 0⁰ = 1/0, thus value of cot 0^o is undefined i.e. equal to infinity.

What is Value of Sin 45^o ?

Value of sin 45° is 1/√2.