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Trigonometric functions are fundamental in mathematics, linking angles and side lengths in right-angled triangles. They include sine, cosine, and tangent, which are graphically represented as waves and curves, and have key values at specific angles. Understanding these functions, along with their inverse and reciprocal counterparts, is essential for applications in various fields such as physics and engineering.

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## Definition and Applications

### Sine, Cosine, and Tangent

These functions define the relationships between angles and sides in a right-angled triangle and have applications in various fields

### Graphical Representations

Sine and Cosine Waves

These functions are represented graphically as sinusoidal waves with a period of 2π radians and oscillate between -1 and 1

Tangent Graph

The tangent function produces a graph with vertical asymptotes and an infinite range

### Mastery of Key Angles

Understanding the values of trigonometric functions at common angles is crucial for proficiency in trigonometry

## Inverse and Reciprocal Functions

### Inverse Functions

Arcsine, arccosine, and arctangent are the inverses of sine, cosine, and tangent, respectively, and are used to determine an angle from a known ratio

### Reciprocal Functions

Cosecant, Secant, and Cotangent

These functions are defined as the reciprocals of sine, cosine, and tangent and are useful in certain integrals and geometric configurations