What is the value of tan inverse of 0?

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.

(image will be uploaded soon)

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

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.

(Image will be uploaded soon)

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

Page 2

In rupees, one billion equals 10,000 lakhs. 1,000,000,000 is a natural number that equals one billion. The number 999,999,999 comes before 1 billion, and 1,000,000,001 comes after it. The concept of place value is used in mathematics to describe quantities. There are two ways to interpret the place value of the digits in a number. The Indian System and the International System are the two. The place value charts are used to determine the number's positional values. With the support of positions, numbers in the general form can be extended.

The place value is ordered from right to left. Starting with the unit location (one's place), the place value progresses to tens, hundreds, thousands, and so on. Let us look at the value of 1 billion in rupees of the Indian scheme of place value and 1 billion dollars in rupees in words. We'll also look at the position value chart for both the Indian and International systems.

Overview of the Topic

The place value is ordered from right to left. Starting with the unit location (one's place), the place value progresses to tens, hundreds, thousands, and so on. Let us look at the value of 1 billion in rupees of the Indian scheme of place value and 1 billion dollars in rupees in words. We'll also look at the position value chart for both the Indian and International systems.

Students get scared by seeing big numbers but nothing to get scared of. It is important that students must understand how to identify big numbers. They must have proper knowledge and information about the rules for identifying big numbers. There are different ways to identify the numbers. Mainly, students are taught about two different systems of place value. One is the Indian system of place value and the other is the International System of place value. It is important that students must have knowledge of both the Indian and the International System of place values to identify big numbers easily. Students must know how to convert international numbers in the Indian system. The names given to different numbers in the Indian and international system are different and students must know this concept for excelling in higher classes. 

1 Billion is a big number and it is equal to 10,000 lakhs in Indian money.  One billion can be written as 1,000,000,000. Students can remember this by counting the zeroes. There are nine zeros in one billion. Similarly, if students want to remember other big numbers they can count the zeroes. For example, one million will have six zeros and it is written as 1000,000. Thus, in a similar manner students can remember other big numbers. 

One Billion in Rupees

Consider 1 dollar = 73.80 rupees

Value of 1 billion = 1,000,000,000 rupees

So 1 billion dollars in rupees = 73.80 x 1,000,000,000 =7.38 x 101010

Similarly

5 billion dollars in rupees =73.80 x 5,000,000,000 = 369 x 101111

1 Billion in Indian Rupees

The International System uses billions based on position value charts. The equivalent value of  1 billion in Indian rupees (according to the Indian System) is

1 billion in rupees = 1,000,000,000 Rupees

We can write it as:

1 Billion = 10,000 Lakhs (As we know 1 lakh = 1,00,000)

As a result, a billion in lakhs equals 10,000 lakhs. It means that one billion lakhs equals ten million lakhs.

In other words, 1 billion equals 100 crores (as 1 lakh equals 1,00,00,000).

Conversion from Billion to Lakhs

Multiply the given billion value by ten thousand lakhs to convert the given billion value to lakhs (10,000 Lakhs)

Multiply 7 by 10,000 lakhs, for example, to convert 7 billion to lakhs.

(i.e.,) 7 Billion = 7 x 10,000 lakhs

70,000 lakhs = 7 billion

As a result, 7 billion equals 70,000 lakhs.

1 billion dollar to inr is 73,80,00,50,000

Conversion from Billion to Crores

Multiply the given billion value by 100 crores to convert the given billion value to crores.

To convert 9 billion to crores, multiply 9 by 100 crores, as an example.

(To put it another way,) 9 billion is equal to 9 x 100 crores.

900 crores = 9 billion dollars

As a result, 9 billion equals 900 crores.

Similarly, any billion value can be converted to values in the Indian numbering system, such as lakhs, crores, and so on.

How Many Zeros in a Billion?

There are nine (9) zeros in a billion. 

1 billion = 1,000,000,000  

How Many Millions is a Billion?

1 million = 1000,000

One million is equal to 1000 thousand.

1 billion = 1000 million = 1000,000,000

Therefore, one billion is equal to 1000 million.

Place Value Chart for Indian System

The sequence of the position value of the digit in the Indian system is as follows:

The Hindu-Arabic method of numeration is also known as the Indian system of numeration. The comma symbol "," is used to differentiate the intervals in this scheme. The first comma appears after three digits from the right hand, followed by two digits, two digits, and then every two digits.

International System Place Value Chart:

The sequence of a digit's position value in the International System is as follows:

Ones

Thousands

Millions

Billions

How to Use the Calculator to Convert Billion to Rupees?

The following is the protocol for using the billion to rupees conversion calculator:

Step 1: In the input region, type the number of billions.

Step 2: To get the conversion value, press the "Convert" button.

Step 3: Finally, in the output sector, the value of the conversion from billions to rupees will be shown.

What Does Billion to Rupees Conversion Mean?

In the Indian and International (more precisely the US) numeral systems, the place value of digits is referred to in various ways. Digits in the Indian system have place values of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, and so on. The position values of digits in the International system are in the order Ones, Tens, Hundreds, Thousands, Ten Thousand, Hundred Thousands, Millions, Billions, and so on. As a result, 1 billion is converted to 100 crores in the conversion from billions to rupees.

1 billion rupees = 1,000,000,000 rupees

Since 1 lakh equals Rs. 100000, 1 billion equals 10,000 lakhs.

100 Crores = 1 Billion

Solved Examples

1. What is the Rupee Equivalent of 5 Billion? 

Solution: We know that a billion rupees equal 1,000,000,000 rupees.

As a result, the rupee value of 5 billion is estimated as follows:

5 Billion = 5 x 1,000,000,000

5 Billion = 5,000,000,000 rupees

We may also assume that 5 billion equals 500 crores.

2. In Crores, What is the Worth of 4.6 Billion?

Solution: We know that

1 Billion = 100 crores

Therefore, 4.6 Billion = 4.6 x 100 crores

4.6 Billion = 460 crores

Hence, the value of 4.6 billion is 460 crores.

Overview of Place Value

Place value is an important concept in mathematics. It helps to determine the position of a digit in the given number. Each digit in a number has a position. A number can be expanded depending on the position of different digits. We count the place value of digits from right to left. The position will start from the unit's place and move on to tens, hundreds, thousands, ten thousand, etc.

The place value of every digit in a given number is different. A number may have two same digits but both digits in the number will have a different position or place value. For example, 5456 in this number 5 will have a different place value. The number on the right will have a place value of tens and the number on the left will have a place value of ten thousand.

Solved Examples

1. What is 3 billion equal to the Indian rupee?

You know that one billion is equal to 1,000,000,000 rupees.

Thus, the value of 3 billion can be calculated as follows:

3 Billion = 3 x 1, 000,000,000

3 Billion = 3,000,000, 000 rupees.

We can also say that 3 million is equal to 300 crores.

Convert 4 billion to lakhs

We know that one Billion is equal to = 10,000 lakhs

Thus the value of 4 billion can be calculated as follows

1 billion = 10,000 lakhs

4 billion = 4 x 10,000

4 billion = 40,000 lakhs

Thus, we can say that the value of 4 billion is 40,000 lakhs