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Tan 0 Degrees

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Last updated date: 27th Feb 2024
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Tan 0 Value

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 0 values and how to derive the tan 0 degrees value.


What is the Value of Tan 0 Degrees Equal to?

The Value of Tan 0 degrees is equal to zero.


Derivation of the Tan 0 Degree

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


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What is 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 = Opposite side/ Hypotenuse.


What is 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 = Adjacent side / Hypotenuse.


What is 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 = Opposite side / Hypotenuse.


Find Tan 0° Using Sin and Cos

Also, the values of the sin of 0° and cos of 0° are used to find the value tan of 0°, but the condition is that sin 0°, and cos 0° must be from the same triangle. It is just a very basic concept of trigonometry to find the tangent of the angle using the sine and cosine of the angle. It is known that the ratio of sine and cosine of the same angle gives the tangent of the same angle. So, if we have the value of sin 0° degree and cos 0° degree, then the value of tan 0° degrees can be calculated very easily.


Accordingly, Tan θ = Sinθ/ Cosθ


Tan 0 degree in fraction can be expressed as,


Tan 0 degrees equal to Sin 0° / Cos 0°


We know than Sin 0 ° = 0 and Cos 0° = 1


Therefore, the Tan 0 is equal to 0/1 or 0.


It implies that Tan 0 is equal to 0.


Trigonometry Equations on the Basis of Tangent Function

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 = Perpendicular/ Base Or Tanθ = Sinθ/ Cosθ Or Tanθ = 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) = - Cotθ


Tan (-θ) = Tanθ


Trigonometry Ratio Table of Different Angles


Angle

30°

45°

60°

90°

180°

270°

360°

sin

0

\[\frac{1}{2}\]



\[\frac{1}{\sqrt{2}}\]





\[\frac{\sqrt{3}}{2}\]





1

0

-1

0

cos

1

\[\frac{\sqrt{3}}{2}\]





\[\frac{1}{\sqrt{2}}\]





\[\frac{1}{2}\]



0

-1

0

1

tan

0

\[\frac{1}{\sqrt{3}}\]





1

\[\sqrt{3}\]




0

1

cot

\[\sqrt{3}\]




1

\[\frac{1}{\sqrt{2}}\]





0

0

csc

2

\[\sqrt{2}\]




\[\frac{2}{\sqrt{3}}\]




1

-1

sec

1

\[\frac{2}{\sqrt{3}}\]





\[\sqrt{2}\]




2

-1

1

 

Questions to be Solved

Evaluate the following questions given below-


Question 1) Tan (90-45)°


Solution: As we know, Tan (90-θ) = Cot θ


Tan (90 - 45) =Cot 45°


Cot 45° = 1


So accordingly,


Tan (90 - 45)° = 1


Hence, the value of Tan (90 - 45)° is 1.


Question 2)  Find the value of Tan 150°


Solution: Tan 150° = Tan (90 + 60)°


As we know,


Tan (90 + θ) = Cosθ


Tan (90 + 45) = Cos 45°


Cos 45° = 1


Accordingly,


Tan (90 + 45)° = 1.


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Tan 0 Value

The three basic functions of trigonometry are Sine, Cosine, and Tangent, through which the  trigonometric identities, the trigonometric functions, and formulas are formed. The tangent can be 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. Tangent function 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.


Hypotenuse side: In a right-angled triangle, it is the opposite side of the right angle. Hypotenuse is the longest side of any right-angled triangle, opposite the right angle. The side that is opposite the angle of interest is called the opposite side and the remaining side is known as the adjacent side, where it forms a side of both the right angle and the angle of interest.


Derivation of the Tan 0 Degree.

The sine function and cosine function is used in order to find the value of tan 0 degrees  as  the tan function is the ratio of the sine function and cos function.


The values of tangent degrees can be found  with the help of the sine functions and cosine functions. By knowing the value of sine functions, we will be able to find the values of cos and tan functions.


The values of the sin of 0° and cos of 0° are used to find the value tan of 0°,  provided sin 0°, and cos 0° is from the same triangle. 


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


Tan θ = Perpendicular/ Base Or Tanθ = Sinθ/ Cosθ Or Tan Θ = 1/Cosθ.


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) = - Cotθ


Tan (-θ) = Tanθ.


The Law of Tangents formula : (α - β)/(α + β) = tan {β - (α/2)}/tan (α+β)/2


FAQs on Tan 0 Degrees

1. How can you explain the Law of Tangents ?

The relationship between the tangent of two angles and the length of the opposite sides is basically the Law of Tangents.It is also applied in the triangles other than the right-angle triangle which  is important as the law of sine and law of cosines. In order to find the remaining parts of a triangle if two angles and one side or two sides and one angle are given in the question, the Law of Tan is used.This is also referred to as SAS (side angle side) or the ASA (angle-side-angle).


To understand the concept of the Law of Tangent, the three important facts of an ordinary triangle are needed.


The value of the remaining parts of the triangle is calculated with the help of the Law of Tangents provided the following points are in the question.


  • Two sides and one opposite angle of any triangle

  • Anyone side and two angle

  • All three sides

  • Any two sides and the angle between them.

2. Explain the three basic functions of Trigonometry?

The Sine Function : For a given right angle triangle, the Sin of angle θ is said to be the ratio of the length of the opposite side of a triangle to its hypotenuse.   Sin θ = Opposite side/ Hypotenuse.


The Cosine Function : For a given right angle triangle, the Cosine of angle θ is said to be the ratio of the length of the adjacent side of a triangle to its hypotenuse.   Cos θ = Adjacent side / Hypotenuse.


The Tangent Function: For a given right angle triangle, the Cosine of angle θ is said to be the ratio of the length of the opposite side of a triangle to the angle and the adjacent side.    Tan θ = Opposite side / Hypotenuse.

3. Mention the important things in this chapter?

Few important points to remember of this chapter are:

  • Tan is one of the commonly used trigonometric functions. 

  • Tangent is defined as the ratio of the opposite side to the adjacent side.

  • Tan 0 Degrees value is zero.

  • According to quotient trigonometric identity, the tan function can be written in terms of sine and cos functions as Tanθ = Sinθ/Cosθ

  • We can derive the value of trigonometric functions using the fundamental method and trigonometric method.

4. What are the different types and functions in Trigonometry?

The branch of mathematics which deals with  the relationship between the sides of a triangle (Right-angled triangle) and its angles is what we understand as Trigonometry.The functions of an angle of a right-angled triangle are referred to as trigonometric(or Circular) functions. The  basic types of trigonometric functions are:

  • Sin function

  • Cos function

  • Tan function

  • Cot function

  • Cosec function

  • Sec function

5. Where can we get study notes for Trigonometry?

Trigonometry is an important and tough subject and it is important to be able to practice some of the important questions to be able to score well. The online portal, Vedantu.com offers important questions along with answers  and other very helpful study material on Trigonometry, that have been formulated in a  well structured, well researched, and easy to understand manner. These study materials and solutions are all important and are very easily accessible from Vedantu.com and can be downloaded for free. 

6. Explain the Law of Tangents

The law of tangent represents the relationship between the tangent of two angles and the length of the opposite sides. The law of tangent is also applied in the triangles other than the right-angle triangle as it is equally important as the law of sine and law of cosines. The law of tan is used to find the remaining parts of a triangle if two angles and one side or two sides and one angle are given in the question which is also referred as SAS (side angle side) or ASA (angle-side-angle) from the perspective of congruence of the triangle.


The three important pieces of information of an ordinary triangle is needed to understand the concept of the law of tangents. The value of the remaining parts of a triangle can be calculated through the concept of law of tangents if any of the information given below is given in the question.

  • Two sides and one opposite angle of any triangle

  • Anyone side and two angle

  • All three sides

  • Any two sides and the angle between them.

Law of Tangents Formula

(α - β)/(α + β) = tan {β - (α/2)}/tan (α+β)/2