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Trigonometry is a mathematical field that examines the relationships between triangle angles and sides, especially in right-angled triangles. It uses sine, cosine, and tangent functions to calculate unknown angles and distances. The mnemonic SOHCAHTOA aids in remembering these relationships, while the Laws of Sines and Cosines extend trigonometry to non-right-angled triangles. Additionally, the unit circle is a fundamental concept for understanding trigonometric functions and their periodic nature.

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## Definition and Functions

### Branch of mathematics

Trigonometry is a branch of mathematics that explores the relationships between angles and sides of triangles

### Primary trigonometric functions

Sine, cosine, and tangent

The primary trigonometric functions, sine, cosine, and tangent, express the relationships between angles and sides of triangles as ratios

Reciprocal functions

The reciprocal functions, cosecant, secant, and cotangent, are the inverse of the primary trigonometric functions

### Importance in solving triangles

Trigonometric functions are crucial for determining unknown angles and distances in right-angled triangles

## Laws and Formulas

### Laws of Sines and Cosines

The Laws of Sines and Cosines are used to solve for unknown sides and angles in general triangles

### Area formula

The formula for calculating the area of any triangle is (1/2)ab sin(C), where 'a' and 'b' are the lengths of the sides and 'C' is the measure of the included angle

## Unit Circle

### Definition and Purpose

The unit circle is a circle with a radius of one unit centered at the origin of a coordinate plane, used to represent trigonometric functions and understand their properties

### Representation of trigonometric functions

Trigonometric functions can be represented as coordinates on the unit circle, with the x-coordinate corresponding to the cosine of an angle and the y-coordinate to the sine

### Insight into trigonometric functions

The unit circle provides insight into the periodic nature of trigonometric functions and their values at various angles

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