[Maths Class Notes] on Tangent Formula Pdf for Exam

The tangent angle formula is one of the formulas that are used to calculate the angle of the right triangle. The tangent function along with the sine and cosine is one of the three most common trigonometric functions. In any triangle the tangent of a triangle can be provided as follows:

Tan θ = [frac {text{Opposite side}} {text{Adjacent side}} ]

Where, O is the opposite side and A the adjacent side.

In such a way students can learn about Tangent Formula – Tangent Function, Derivation, Trigonometry Ratio, and Questions Solved via .

Learn Tangent Formula

Sine, Cosine, and Tangent are the three basic functions of trigonometry through which trigonometric identities, trigonometry functions, and formulas are formed. The tangent is defined as the ratio of the length of the opposite side or perpendicular of a right angle to the angle and the length of the adjacent side. The tangent function in trigonometry is used to calculate the slope of a line between the origin and a point defining the intersection between hypotenuse and altitude of a right-angle triangle. In this article, we will discuss the tan formula, the formula of a tangent.

 

What is Trigonometry?

It is the study of the relationships which involve angles, lengths, and heights of triangles given. It also relates to the different parts of circles as well as other geometrical figures. Trigonometry has many trigonometric ratios which are very fundamental in mathematics. It has many identities that are very useful for learning and deriving the many equations and formulas in science. There are many fields where these identities of trigonometry and formulas of trigonometry are useful.

 

What is the Tangent Function?

Tangent is the ratio of the opposite side divided by the adjacent side in a right-angled triangle. In trigonometry, there are six possible ratios. A ratio is a comparison of two numbers i.e. sides of a triangle. The Greek letter,θ, will be used to represent the reference angle in the right triangle. These six ratios are useful in different ways to compare two sides of a right triangle.

 

Tan Formula is normally useful to calculate the angle of the right triangle. In a right triangle or the right-angled triangle, the tangent of an angle is a simple ratio of the length of the opposite side and the length of the adjacent side. Tangent is usually denoted as ‘tan’, but it is pronounced as a tangent. This function is useful to find out the length of a side of a triangle. It is possible when someone knows at least one side of the triangle and one of the acute angles.

 

Derivation of the Tan Formula

As we know, Sine, Cosine, and Tangent are the three basic functions of trigonometry. Let us briefly all the three basic functions with the help of a right-angle triangle.

 

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What is the Sine Function?

The Sine Function states that for a given right angle triangle, the Sin of angle θ is defined as the ratio of the length of the opposite side of a triangle to its hypotenuse.

 

Sin θ = [ frac{text{Opposite side}}{Hypotenuse} ]

 

What is the Cosine Function?

The Cosine Function states that for a given right angle triangle, the Cosine of angle θ is defined as the ratio of the length of the adjacent side of a triangle to its hypotenuse.

 

Cos θ = [ frac {text{Adjacent side}} {Hypotenuse} ]

 

What is the Tangent Function?

The Tangent Function states that for a given right angle triangle, the Cosine of angle ϴ is defined as the ratio of the length of the opposite side of a triangle to the angle and the adjacent side.

 

Tan θ =[ frac{text{Opposite side}} {Hypotenuse}]

 

Trigonometry Equations on the Basis of Tangent Function (Tangent Formulas)

Various tangent formulas can be formulated through a tangent function in trigonometry. The basic formula of the tangent which is mostly used is to solve questions is,

 

Tan θ = [ frac{Perpendicular}{Base}] or Tanθ = [ frac{Sinθ}{Cosθ}] or Tanθ = [ frac{1}{Cotθ}]

 

Other Tangent Formulas are

Tan (a+b) equals Tan (a) + Tan (b)/1- Tan (a) Tan (b)

 

Tan (90 + θ) = Cot θ

 

Tan (90 – θ) = – Cot θ

 

Tan (-ϴ) = Tanθ

 

Trigonometry Ratio Table of Different Angles

 

Questions to be Solved 

Question 1

Calculate the tangent angle of a right triangle whose adjacent side and opposite sides are 8 cm and 6 cm respectively?

Solution

Given, Adjacent side i.e. base = 8 cm

Opposite side i.e. perpendicular = 6 cm

Also, the tangent formula is: Tan θ=perpendicular/base

Tan θ=6/8 = 0.75

Therefore, tan θ=0.75

Thus the tangent value will be 0.75.

 

Question 2

Calculate the tangent angle of a right triangle whose adjacent side and opposite sides are 10 cm and 4 cm respectively?

Solution

Given, Adjacent side i.e. base = 10 cm

Opposite side i.e. perpendicular = 4 cm

Also, the tangent formula is: Tan θ=perpendicular/base

Tan θ=10/4 = 2.5

Therefore, tan θ= 2.5

Thus the tangent value will be 2.5.