pythagoras theorem

Pythagoras Theorem (also called Pythagorean Theorem) is an important topic in Math, which makes sense of the connection between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples. The formula and proof of this theorem are explained here with examples.

Pythagoras Theorem is essentially used to track down the length of an obscure side and the point of a triangle. By this Theorem, we can derive the base, perpendicular and hypotenuse formulas. Allow us to get familiar with the arithmetic of the Pythagorean hypothesis exhaustively here.

Pythagoras Theorem Statement

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

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Basic Concept of Trigonometry Class 10

Basic Concept of Trigonometry Class 10

some technique to remember Formulae in easy way. Follow this video without interruption.

Hello Students,

I am Abid Your Tutor / Mentor , Today's I came here to discuss about Class 10th Trigonometry and function.

How Trigonometry Derived and what is the purpose of trigonometry in Math Subject Class 10.

We have given Detail information of Trigonometry in this video.

You will get to learn in depth about Trigonometry 

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Trigonometry Ratio

Definition: Trigonometry is about triangles or to be more exact the connection between the points and sides of a sides of a right-angled triangle. There are three sides of a triangle named Hypotenuse, Adjacent, and Opposite. The proportion between these sides in view of the point between them is called Trigonometric Proportion.

As given in the figure in a right-angle triangle 

• The side opposite the right angle is called the hypotenuse
• The side opposite to an angle is called the opposite side
  • For angle C opposite side is AB
  • For angle A opposite side is BC
• The side adjacent to an angle is called the adjacent side
• For angle C adjacent side is BC
• For angle A adjacent side is AB

What are Trigonometric Ratios?

There are 6 basic trigonometric relations that form the basics of trigonometry. These 6 trigonometric relations are ratios of all the different possible combinations in a right-angled triangle.

These trigonometric ratios are called 

• Sine
• Cosine
• Tangent
• Cosecant
• Secant
• Cotangent

The mathematical symbol θ is used to denote the angle.

Sine (sin)

Sine of an angle is defined by the ratio of lengths of sides which is opposite to the angle and the hypotenuse. It is represented as sin θ

Cosine (cos)

Cosine of an angle is defined by the ratio of lengths of sides which is adjacent to the angle and the hypotenuse. It is represented as cos θ

Tangent (tan)

Tangent of an angle is defined by the ratio of the length of sides which is opposite to the angle and the side which is adjacent to the angle. It is represented as tan θ

Cosecant (cosec)

Cosecant of an angle is defined by the ratio of the length of the hypotenuse and the side opposite the angle. It is represented as cosec θ

Secant (sec)

Secant of an angle is defined by the ratio of the length of the hypotenuse and the side and the side adjacent to the angle. It is represented as sec θ

Cotangent (cot)

Cotangent of an angle is defined by the ratio of the length of sides that is adjacent to the angle and the side which is opposite to the angle. It is represented as cot θ.

Trigonometric Ratios Table

Trigonometric ratios for any specific angle ‘θ’ is given below:

Angles	0°	30°	45°	60°	90°
sin	0	1/2	1/√2	√3/2	1
cos	1	√3/2	1/√2	1/2	0
tan	0	1/√3	1	√3	Not Defined
cosec	Not Defined	2	√2	2/√3	1
sec	1	2/√3	√2	2	Not Defined
cot	Not Defined	√3	1	1/√3	0 Solving for a Side in Right Triangles with Trigonometric Ratio This is one of the most basic and useful uses of trigonometry using the trigonometric ratios mentioned to find the length of a side of a right-angled triangle but to do, so we must already know the length of the other two sides or an angle and length of one side. Steps to follow if one side and one angle are known: Choose a trigonometric ratio that contains the given side and the unknown side Use algebra to find the unknown side Example: In a right-angled triangle, ABC ∠B = 90° and ∠C = 30° length of side AB is 4 find the length of BC given tan 30° = 1/√3.  Solution: C = 30° tan C = tan 30°          = 1/√3 tan C = opposite side/adjacent side  1/√3 = AB/BC  1/√3 = 4/BC     BC = 4√3 Steps to follow if two sides are known: Mark the known sides as adjacent, opposite, or hypotenuse with respect to any one of the acute angles in the triangle. Decide on which trigonometric ratio can be found from the above table. Find the angle (X) Use a trigonometric ratio with respect to X which is a ratio of a known side and an unknown side. Use algebra to find the unknown side. Example: If two sides of a right-angled triangle are 20 and 10√3 where the side with length 20 is the hypotenuse, find the third side (without using Pythagoras theorem) given sin 30° = 1/2 and cos 30° = √3/2 Solution: hypotenuse = 20 adjacent side = 10√3 cos θ = adjacent side / hypotenuse          = 10√3 / 20      θ  = √3/2

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NCERT Solutions for Class 12 Maths Chapter 2 – Free PDF Download

Inverse trigonometric functions are simply described as the inverse functions of the basic trigonometric functions which might be sine, cosine, tangent, cotangent, secant, and cosecant functions. 

They're additionally termed as arcus functions , antitrigonometric functions or cyclometric functions. These inverse features in trigonometry are used to get the angle with any of the trigonometry ratios. The inverse trigonometry functions have predominant packages in the field of engineering, physics, geometry and navigation. 

 What are Inverse Trigonometric Functions? 

Inverse trigonometric functions are also called “Arc Functions” since, for a given value of trigonometric functions, they produce the length of arc needed to obtain that particular value. The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle. These six important functions are used to find the angle measure in the right triangle when two sides of the triangle measures are known.

Formulas

The basic inverse trigonometric formulas are as follows:

Inverse Trig Functions	Formulas
Arcsine	sin-1(-x) = -sin-1(x), x ∈ [-1, 1]
Arccosine	cos-1(-x) = π -cos-1(x), x ∈ [-1, 1]
Arctangent	tan-1(-x) = -tan-1(x), x ∈ R
Arccotangent	cot-1(-x) = π – cot-1(x), x ∈ R
Arcsecant	sec-1(-x) = π -sec-1(x), |x| ≥ 1
Arccosecant	cosec-1(-x) = -cosec-1(x), |x| ≥ 1

Inverse Trigonometric  Functions Graphs

There are particularly six inverse trig functions for each trigonometry ratio. The inverse of six important trigonometric functions are:

• Arcsine
• Arccosine
• Arctangent
• Arccotangent
• Arcsecant
• Arccosecant

Let us discuss all the six important types of inverse trigonometric functions along with its definition, formulas, graphs, properties and solved examples.

Arcsine Function

Arcsine function is an inverse of the sine function denoted by sin-1x. It is represented in the graph as shown below:

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