Question

What is Trigonometry??​

Answer 1

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Step-by-step explanation:

Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

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Answer 2

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What is Trigonometry?

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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°.

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Trigonometry is one of the important branches in the history of mathematics and this concept is given by a Greek mathematician Hipparchus.

Trigonometry can be divided into two sub-branches:

• Plane trigonometry
• Spherical geometry

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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.

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Six Important Trigonometric Functions

The six important trigonometric functions (trigonometric ratios):

Functions

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

Abbreviation

• sin
• tan
• cos
• cosec
• sec
• cot

Relationship to sides of a right triangle

• Opposite side/ Hypotenuse
• Opposite side/ Adjacent side
• Adjacent side / Hypotenuse
• Hypotenuse / Opposite side
• Hypotenuse / Adjacent side
• Adjacent side / Opposite side

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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.
• 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)

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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

2. 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

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Trigonometry Identities

The three important trigonometric identities are:

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

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Hopes it's helpful and satisfy you.