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Trigonometric functions such as sine, cosine, and tangent are fundamental in mathematics, revealing the relationship between angles and lengths. Their graphs display periodic patterns, characterized by features like amplitude and period. The sine and cosine functions oscillate with an amplitude of 1 and a period of 2π, while tangent has a period of π. Reciprocal functions and their inverses also play a crucial role in understanding trigonometry.

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## Trigonometric Functions

### Primary Trigonometric Functions

The primary trigonometric functions, sine, cosine, and tangent, along with their reciprocals, cosecant, secant, and cotangent, exhibit periodic behavior and can be visualized through their graphs

### Amplitude and Period

The amplitude and period of a trigonometric function can be determined from its standard form and reflect the vertical stretch and horizontal length of the function's pattern

### Domain and Range

The domain and range of trigonometric functions vary, with sine and cosine defined for all real numbers and tangent defined for all real numbers except at odd multiples of π/2

## Graphing Trigonometric Functions

### Construction of Graphs

Trigonometric functions can be graphed by identifying the amplitude and period, constructing a table of values, and plotting significant points on a coordinate plane

### Unit Circle

The unit circle can be used as a reference for determining values at key angles for sine and cosine functions

### Characteristics of Graphs

The graphs of sine and cosine functions exhibit a wave pattern with a period of 2π radians and an amplitude of 1, while the tangent function has vertical asymptotes and a period of π radians

## Reciprocal Trigonometric Functions

### Construction of Graphs

The graphs of reciprocal trigonometric functions, such as cosecant, secant, and cotangent, are derived from the graphs of their primary counterparts

### Domain and Range

The domain of reciprocal trigonometric functions excludes the zeros of their corresponding functions, and their range is all real numbers except for a specific interval

## Inverse Trigonometric Functions

### Definition and Purpose

Inverse trigonometric functions, such as arcsine, arccosine, and arctangent, provide the angle corresponding to a given trigonometric ratio

### Restricted Domains and Ranges

The domains and ranges of inverse trigonometric functions are restricted to principal values, and their graphs reflect the restricted functions across the line y=x

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