Question

can anyone help me to understand the full trigonometry chapter class 8​

Answer 1

Answer:

kindly tell the name of book you have so i can explain you

Step-by-step explanation:

Answer 2

Answer:

Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus. Here, we will study the relationship between the sides and angles of a right-angled triangle. The basics of trigonometry define three primary functions which are sine, cosine and tangent.

Trigonometry is one of those divisions in mathematics that helps in finding the angles and missing sides of a triangle with the help of trigonometric ratios. The angles are either measured in radians or degrees. The commonly used trigonometry angles are 0°, 30°, 45°, 60° and 90°.

Trigonometry can be divided into two sub-branches called plane trigonometry and spherical geometry. Here, you will learn about the trigonometric formulas, functions and ratios, etc.

Trigonometry Ratios-Sine, Cosine, Tangent

The trigonometric ratios of a triangle are also called the trigonometric functions. Sine, cosine, and tangent are 3 important trigonometric functions and are abbreviated as sin, cos and tan. Let us see how are these ratios or functions, evaluated in case of a right-angled triangle.

Consider a right-angled triangle, where the longest side is called the hypotenuse, and the sides opposite to the hypotenuse are referred to as the adjacent and opposite sides.

Six Important Trigonometric Functions

The six important trigonometric functions (trigonometric ratios) are calculated using the below formulas and considering the above figure. It is necessary to get knowledge about the sides of the right triangle because it defines the set of important trigonometric functions.

Functions  Abbreviation  Relationship to sides of a right triangle

Sine Function sin Opposite side/ Hypotenuse

Tangent Function tan Opposite side / Adjacent side

Cosine Function cos Adjacent side / Hypotenuse

Cosecant Function cosec Hypotenuse / Opposite side

Secant Function sec Hypotenuse / Adjacent side

Cotangent Function cot Adjacent side / Opposite side

Trigonometry Angles

The trigonometry angles which are commonly used in trigonometry problems are  0°, 30°, 45°, 60° and 90°. The trigonometric ratios such as sine, cosine and tangent of these angles are easy to memorize. We will also show the table where all the ratios and their respective angle’s values are mentioned. To find these angles we have to draw a right-angled triangle, in which one of the acute angles will be the corresponding trigonometry angle. These angles will be defined with respect to the ratio associated with it.

For example, in a right-angled triangle,

Sin θ = Perpendicular/Hypotenuse

or θ = sin-1 (P/H)

Similarly,

θ = cos-1 (Base/Hypotenuse)

θ = tan-1 (Perpendicular/Base)

Trigonometry Table

Check the table for common angles which are used to solve many trigonometric problems involving trigonometric ratios.

Angles 0° 30° 45° 60° 90°

Sin θ 0 ½ 1/√2 √3/2 1

Cos θ 1 √3/2 1/√2 ½ 0

Tan θ 0 1/√3 1 √3 ∞

Cosec θ ∞ 2 √2 2/√3 1

Sec θ 1 2/√3 √2 2 ∞

Cot θ ∞ √3 1 1/√3 0

In the same way, we can find the trigonometric ratio values for angles beyond 90 degrees, such as 180°, 270° and 360°.

Unit Circle

The concept of unit circle helps us to measure the angles of cos, sin and tan directly since the centre of the circle is located at the origin and radius is 1. Consider theta be an angle then,

Suppose the length of the perpendicular is y and of base is x. The length of the hypotenuse is equal to the radius of the unit circle, which is 1. Therefore, we can write the trigonometry ratios as;

Sin θ y/1 = y

Cos θ x/1 = x

Tan θ y/x

List of Trigonometry Formulas

The Trigonometric formulas or Identities are the equations which are true in the case of Right-Angled Triangles. Some of the special trigonometric identities are given below –

1.Pythagorean Identities

• sin²θ + cos²θ = 1

• tan2θ + 1 = sec2θ

• cot2θ + 1 = cosec2θ

• sin 2θ = 2 sin θ cos θ

• cos 2θ = cos²θ – sin²θ

• tan 2θ = 2 tan θ / (1 – tan²θ)

• cot 2θ = (cot²θ – 1) / 2 cot θ

Sum and Difference identities-

     For angles u and v, we have the following relationships:

• sin(u + v) = sin(u)cos(v) + cos(u)sin(v)
• cos(u + v) = cos(u)cos(v) – sin(u)sin(v)
• tan(u+v) = tan(u) + tan(v)1−tan(u) tan(v)
• sin(u – v) = sin(u)cos(v) – cos(u)sin(v)
• cos(u – v) = cos(u)cos(v) + sin(u)sin(v)
• tan(u-v) = tan(u) − tan(v)1+tan(u) tan(v)

3.If A, B and C are angles and a, b and c are the sides of a triangle, then,

Sine Laws

• a/sinA = b/sinB = c/sinC

Cosine Laws

• c2 = a2 + b2 – 2ab cos C
• a2 = b2 + c2 – 2bc cos A
• b2 = a2 + c2 – 2ac cos B

Trigonometry Identities

The three important trigonometric identities are:

• sin²θ + cos²θ = 1

• tan²θ + 1 = sec²θ

• cot²θ + 1 = cosec²θ

I HOPE IT HELPS!!!!!!