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

The formula of Trigonometry: Trigonometry is a well-acknowledged name in the geometric domain of mathematics, which is in relevant in this domain for ages and is also practically applied across several occasions.

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

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

Formula 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 to have easy calculations.

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

1. Trigonometry Basic Formula

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

3. Pythagorean Identities

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

A dd– Sugar–To –Coffee

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 Identities – Shifting Angles by 𝛑/2, 𝛑, 3𝛑/2

9. Angle Sum & Difference Identities

10. Double Angle Formula

11. Triple Angle Formula

12. Half Angle Identities

13. Sum Identities

14. Product Identities

15. Law of Sin

Here,

• ABC are the vertices of the triangle 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

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

19. Inverse Trigonometry Formula

20. 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 their sides.

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

FAQs related to formulas of trigonometry

Q: What are the basic trigonometric functions?

A: The basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions relate the ratios of the sides of a right-angled triangle to the angles in the triangle.

Q: What is the formula for sin?

A: The formula for sin is: sin(x) = opposite/hypotenuse, where x is the angle opposite to the side whose length is the “opposite” and the hypotenuse is the longest side of the right-angled triangle.

Q: What is the formula for cos?

A: The formula for cos is: cos(x) = adjacent/hypotenuse, where x is the angle adjacent to the side whose length is the “adjacent” and the hypotenuse is the longest side of the right-angled triangle.

Q: What is the formula for tan?

A: The formula for tan is: tan(x) = opposite/adjacent, where x is the angle opposite to the side whose length is the “opposite” and adjacent is the side next to it.

Q: What is the formula for cot?

A: The formula for cot is: cot(x) = adjacent/opposite, where x is the angle adjacent to the side whose length is the “adjacent” and opposite is the side next to it.

Q: What is the formula for sec?

A: The formula for sec is: sec(x) = hypotenuse/adjacent, where x is the angle adjacent to the side whose length is the “adjacent” and the hypotenuse is the longest side of the right-angled triangle.

Q: What is the formula for csc?

A: The formula for csc is: csc(x) = hypotenuse/opposite, where x is the angle opposite to the side whose length is the “opposite” and the hypotenuse is the longest side of the right-angled triangle.

Q: How are these trigonometric functions related to each other?

A: The functions sin, cos, tan, cot, sec, and csc are all related to each other through various trigonometric identities, such as the Pythagorean identity, reciprocal identities, quotient identities, and others.

Q: Can these trigonometric functions be used to solve real-world problems?

A: Yes, trigonometric functions are used extensively in fields such as physics, engineering, surveying, navigation, and many others to solve real-world problems related to angles, distances, and heights.