Trigonometry Table

Aug 08, 2022, 16:45 IST

The word Trigonometry is derived from the Greek words Trigonometria meaning Triangle measuring. In fact Trigonometry is the study of relationship between the sides and angles of the triangle. In this chapter, we will study some ratio of the sides of a right triangle with respect to its acute angles, called trigonometric ratios of the angle.We will restrict our discussion to acute angle only.However, these ratios can be extended to other angles also.We will also define the trigonometric ratios for angles of measure 0^o and 90^o.We will calculate trigonometric ratios for some specific angles and establish some identities involving these ratios called Trigonometric identities.

Trigonometry is a subsidiary branch of Mathematics. It mainly comprises the study of angles, lengths and relationship with other angles. Many times students face significant issues in comprehending with these all aspects. Here the team at Physics Wallah has come with an exhaustive Trigonometry table for students. This table mainly comprises of right angles and its other subsidiary angles.

The significance of Trigonometry table lies back to ancient times and crucial even today. This table holds significant importance in scientific as well as mathematical calculations. This calculation can be easily calculated by learning this table. Many geometric calculations can be easily figured out using the table of Trigonometric functions and formulas as well.

Why Trigonometry is important?

These applications to this table are not only limited to class 12th, but also professional courses like engineering. Students need to be aware of the fact that the foundations of first mechanical devices were laid on the basis of these tables.

The trigonometric values can be of great use when considering complex calculations. Even today very high-end calculations of satellites and rockets are done on the basis of trigonometric values. The ease to determine values for different angles has made this table most popular. Memorising these Trigonometry tables is an important aspect for student’s appearing for examinations. This table not only accurate your answer but also makes your calculations faster enough. Through one can get to know how interlinked trigonometric values and formulas are.

Through Trigonometry table one can easily find values of 0°, 30°, 45°, 60° and 90° with ease. These table has been very effective when there were no electronic calculators. These formulas are very easy to remember and students keep all the values right at their tips of the tongue. The prominent functions like Cos, Sine, Tan, Cot, Cosec, Sec can be easily determined through this table. The team at Physics Wallah comprises of experts with immense experience in offering qualities assistance to students. Do solve Trigonometric questions prepared by experts.

How to Study Trigonometric table effectively?

This Trigonometry table is a beneficiary not only for schools or board examination but also for the competitive examination. Students with complete knowledge of Trigonometry table can score higher marks compared to their counterparts. The team at Physics Wallah comprises of experts who have aced various national level examinations. Through this table, students can create a significant effect on their All India Ranks.

The team has not only provided a complete Trigonometry table for students but also provided tricks to remember it. Most of the students are unable to recall the values of the table and end up losing easy marks.

Why Physics Wallah is best for Trigonometric tricks?

Students can directly download the complete and accurate table from the website of Physics Wallah. In order to make sure students can comfortably learn each and every aspect. The team has also provided secret tips and tricks to solve critical problems with trigonometric values.

The very ideology of making education accessible to all. The team at Physics Wallah has checked has all the values in Trigonometry table for any discrepancy. We have provided a complete table for free of cost. Students can download a complete table with just a single click. All that students need to do is to sign up with us. Climb the ladders to success with Physics Wallah.

Trigonometric Ratios Table of 0 and 90

Let us see what happens to the trigonometric ratios of angle A, If is made smaller and smaller in the right triangle ABC. The point c gets closer to point B, and finally when ÐA becomes very close to 0^o, AC becomes almost the same as AB.

About Trigonometry Table

Trigonometry is one of the most ancient subjects studied by scholars all over the world.The astronomers used trigonometry to calculate distance from the Earth to the planets and stars.Trigonometry is also used in geography to construct maps, determine the position of an island in relation to the longitudes and latitudes, etc.

Topics To be covered

• Trigonometric ratios
• Trigonometry identities
• Trigonometry angles
• Complimentary relations
• Other trigonometry relations
• Height and Distance

Let A be the top of a tower and C be the eye of a person from where he is observing the top of a tower, then AC is called the line of sight.The angle so formed by the line of sight with the horizontal level is called the angle of elevation of the top of tower from the eye of a person. Do read NCERT text book and solve questions take help form Physics Wallah NCERT solutions for class 10 Maths.

Hence, the line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer, i.e., the angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level.Let C be an object and A be the eye of a person from where he is observing the object C, then AC is called the line of sight.The angle ,so formed by the line of sight with the horizontal level is called the angle of depression of the object fro the eye of a person.Hence, the line of sight is the line drawn from the eye of angle observer to the point in the object viewed by the observer, i.e., the angle so formed by the line of sight with the horizontal level is called the angle of depression. The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal level when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed.

Now, in a right △ABC, we have

BC || AD and AC is a transversal

∠ACB = ∠CAD

∠θ = ∠θ

Hence, Angle of elevation = Angle of Depression

Use of Trigonometry Table

Academic team of Physics Wallah eleborate the use of Trigonometry Table in the following pdf . how to solve the numerical by using proper use of Trigonometry Table.It will be highly suggested that students must memorise Trigonometry Table for future reference .Trigonometry Table is used in all most all chapters of Trigonometry in all class so read the theory of Trigonometry in detail. Refer Trigonometry Table and Trigonometry Questions prepared by Physics Wallah.

Trigonometric Functions of Complementary Angles

Before starting, it is better to try and memorize these values ​​and know the following trigonometric formulas. Because if you are well aware of the patterns beforehand, it will be easy for you to attempt the questions. Each function is related to its corresponding function. As in the formulas below, you will find that the sin function is related to the cos function and vice versa. Furthermore, the is function is related to the tan function and vice versa. The second function of the sec is also related to the function of the crib and vice versa.

• sin x = cos (90°− x)
• cos x = sin (90°− x)
• tan x = cot (90°− x)
• cot x = tan (90°− x)
• sec x = cot (90°− x)
• cot x = sec (90°− x)
• 1/sin x = 1/cos x = sin x
• 1/cos x = sec x
• 1/sec x = cos x
• 1/tan x = cot x
• 1/cot x = tan x

Trigonometric Identities

The word Trigonometry means ‘three angles measurement’. It is derived from greek words tri, gonia, metron, tri means three, gonia means an angle and metron means measure.

Angle

An angle is the amount of rotation of a revolving line with respect to a fixed line.

Note : If the rotation is in clockwise sense, the angle measured is negative and it is positive in the rotation is in anti–clockwise sense.

Do solve questions of Trigonometry for practice.

Different Units for Measuring Angles

Sexagesimal system (or) British system

In sexagesimal system, a right angle is divided into 90 equal parts called degrees. Further, each degree is divided into sixty equal parts called minutes and each minute is divided into sixty equal parts called seconds.

Thus, 1 right angle = 90 degrees (90°)

1° = 60 minutes (60¢)

1¢ = 60 seconds (60¢¢)

Centesimal system or French system

1 right angle is divided into 100 equal parts. Each part is called a grade.

1 right angle = 100 grades (100^g)

1 grade = 100 minutes (100¢)

1 minute = 100 seconds (100¢¢)

Radian Measure

An angle made by an arc of length equal to radius of a given circle at its centre is called one Radian.

Relation between degree and radian.

If D is the degree measure of an angle and R is its measure in Radians.

Important Trigonometry formulas

1. In a right-angled triangle

ON = x, NP = y and OP = r, ∠PON = θ, ∠PNO = 90

• sinθ = opposite side / hypotenuse = NP/OP = y/r
• cosθ = adjacent side / hypotenuse = ON/OP = x/r
• tanθ = Opposite side / Adjacent side = NP/ON = y/x
• cosecθ = Hypotenuse / Opposite side = OP/NP = r/y
• secθ = Hypotenuse / Adjacent side = OP/ON = r/x
• cotθ = Adjacent side / Opposite side = ON/NP = x/y

2. sinθ.cosecθ = 1 = sin = 1/cosecθ = 1/ sinθ

3. cosθ.secθ = 1 = cosθ = 1/secθ = cotθ = 1/cosθ

4. tanθ.cotθ = 1 = tanθ = 1/cotθ = cotθ = 1/tanθ

5. tanθ = sinθ/cosθ

6. cotθ = cosθ/sinθ

For all values of θ

• sin²θ + cos²θ = 1
• sec²θ - tan²θ = 1
• cosec²θ - cot²θ = 1

Frequently Asked Question (FAQs)

Q1. How to learn Trigonometry Table

Ans. Read the Following Steps mention below:

1. Create a table of Trigonometry. Draw your table to have six rows and six columns.
2. Fill in the values for the sine column. Use the value √x/2 to fill in the blank entries in this column.
3. Now, Place the sine column entries in the cosine column in reverse order. Mathematically, sin x° = cos (90-x)° for any x value.
4. Divide your sine values by the cosine values to fill the tangent column. we know, tangent = sine/cosine.
5. Reverse the entries values in the sine column to find the cosecant of an angle.
6. Place the entries values from the cosine column in reverse order in the secant column.
7. Now, Fill the cotangent column by reversing the values from the tangent column.

Q2. How do you remember the trigonometric table?

Ans. To keep in mind the trigonometric table, use the acronym "SOHCAHTOA". The full form of "SOHCAHTOA" is Sine opposite hypotenuse, adjacent cosine hypotenuse, tangent opposite adjacent. For example, in case you wanted to calculate the sine of an angle or triangle, you should have to know that sine is "sine opposite hypotenuse" primarily based totally on "SOHCAHTOA.".

Q3. What are the ratios of the trigonometric table?

Ans. The trigonometric table consists of the following trigonometric ratios i.e, sine, cosine, tangent, cosecant, secant, cotangent. The following ratios can be written as sin, cos, tan, cosec, sec and cot.