Formulas of Trigonometry – [Sin, Cos, Tan, Cot, Sec & Cosec]

Trigonometry is a well acknowledged name in the geometric domain of mathematics, which is in relevance in this domain since ages and is also practically applied across the number of occasions.

In simple language trigonometry can be defined as that branch of algebra, which is concerned with the triangle. In this branch we basically study the relationship between angles and side length of a given triangle. With this detailed study of triangle, several types of equations are formed, which are consequently solved to simplify the relationship between the side and angle lengths of such triangle.

Trigonometry is considered as one of the oldest components of Algebra, which has been existing around since 3rd century. There are the practical usages of trigonometry in several contexts such as in the domain of astronomy,surveying, optics or in periodic functions.

Formulas of Trigonometry

Well, whether it is algebra or geometry both of these mathematics branches are based on scientific calculations of equations and we have to learn the different formulas in order to have its easy calculation.

As we know that in Trigonometry we basically measure the different sides of a triangle, by which several equations are formed. Further the formulas of Trigonometry are drafted in accordance to the various ratios used in the domain, such as sine, tangent, cosine etc. So, basically there are the numbers of the formulas which are generally used in Trigonometry to measure the sides of the triangle.

Here below we are mentioning the list of different types of formulas of Trigonometry.

  1. Trigonometry Basic Formula

Trigonometry Basic Formula

2. Sin Cos Tan at 0, 30, 45, 60 Degree

Sin Cos Tan at 0, 30, 45, 60 Degree

3. Pythagorean Identities

Pythagorean Identities

4. Sign of Sin, Cos, Tan in Different Quadrants

Sign of Sin, Cos, Tan

A dd– S ugar–T o –C offee

Sign of Sin, Cos, Tan in Different Quadrants

5. Radians

1 Degree = 60 Minutes
Ex:   1 °= 60′

1 Minute = 60 Seconds
Ex:   1′ =  60”

6. Negative Angles [Even-Odd Identies]

Sin (-x) = – Sin x
Cos (-x) = Cos x
Tan (-x) = – Tan x
Cot (-x) = – Cot x
Sec (-x) = Sec x
Cosec (-x) = – Cosec x

7. Value of Sin, Cos, Tan repeat after 2𝛑

Sin (2𝛑 + x) = Sin x
Cos (2𝛑 + x) = Cos x
Tan (2𝛑 + x) = Tan x

8. Periodicity Identies – Shifting Angles by 𝛑/2, 𝛑, 3𝛑/2

9. Angle Sum & Difference Identies

Angle Sum & Difference Identies

10. Double Angle Formula

Double Angle Formula

11. Triple Angle Formula

Triple Angle Formula

12. Half Angle Identies

hALF Angle Formula

13. Sum Identies

Sum Identies

14. Product Identies

Product Identies

15. Law of Sin

Law of Sin

Here,

  • ABC are the vertices of the tringle ABC.
  • The opposite site of angle A is a. i.e. BC
  • The opposite site of angle B is b. i.e. AC
  • The opposite site of angle C is c. i.e. AB

16. Law of Cosine

Law of Cosine

 

17. Inverse Trigonometric Function

If Sin θ = x

then Put Sin on the right side

So, By this, you can see that Sin is an angle, Same as Inverse of all Trignomentry function is an angle.

18. Domain and Range of Inverse Trigonometry Functions

Domain and Range of Inverse Trignometry Functions

19. Inverse Trigonometry Formula

Inverse Trigonometry Formula

Inverse Trigonometry FormulaInverse Trigonometry Formula

Inverse Trigonometry Formula

20. Inverse Trigonometry Substitution

Inverse Trigonometry Substitution

Just like any other branch of mathematics, the formulas of Trigonometry are equally important, since without these formulas you can’t put the values of triangles for the measurement purpose. These formulas are what simplifies the sides of triangles so that you can easily measure all its sides.

We urge all the scholars to understand these formulas and then easily apply them to solve the various types of Trigonometry problems.

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