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 0o, 30o, 45o, 60o, and 90o.
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.
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
Also Check,
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 0o to 360o. 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,
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.
Similar Reads
Trigonometric Graph Trigonometric functions study the relationship between the lengths, heights, and angles of right triangles. As the name implies, trigonometry is referred to as the study of triangles.There are six trigonometric ratios or functions, which are one of the simplest periodic functions. Sine, cosine, and
12 min read
Trigonometric Ratios There are three sides of a triangle Hypotenuse, Adjacent, and Opposite. The ratios between these sides based on the angle between them is called Trigonometric Ratio. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).As give
4 min read
Trigonometric Functions Trigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides.Trigonometric functions are the basic functions used in trigonometry and they are used for solving various types of problems in
6 min read
Trigonometric Cheat Sheet Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles. However, trigonometry can also be challenging to learn and remember, especially when dealing with complex problems and formulas. That is why having a trigonometric cheat sheet can be v
8 min read
Six Trigonometric Functions Trigonometry can be defined as the branch of mathematics that determines and studies the relationships between the sides of a triangle and the angles subtended by them. Trigonometry is used in the case of right-angled triangles. Trigonometric functions define the relationships between the 3 sides an
3 min read
Sin Cos Tan Values Sine (sin), Cosine (cos), and Tangent (tan) are fundamental trigonometric functions that describe relationships between the angles and sides of a right-angled triangle. These are the basic ratios of Trigonometry that are used to study the relationship between the angles and respective sides of a tri
7 min read