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Explore the fundamentals of geometry, focusing on triangles and circles, their properties, and their role in trigonometry. Understand angles in standard position, quadrants of the Cartesian plane, reference angles, and the unit circle. Learn how these concepts are crucial for defining trigonometric functions and their graphs, which are pivotal in mathematics.

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## Triangles

### Definition and Characteristics

Triangles are polygons with three edges and three vertices, formed by connecting three line segments end-to-end

### Trigonometry and Relationships

Trigonometric Functions

Trigonometric functions such as sine, cosine, and tangent explore the relationships between the angles and lengths of triangles

Unit Circle

The unit circle is a fundamental tool in trigonometry that provides a geometric representation of the trigonometric functions

### Angles and Coordinate Plane

Angles in standard position can be used to define trigonometric functions and understand the relationship between angles and the coordinate plane

## Circles

### Definition and Characteristics

Circles are defined by a set of points in a plane that are equidistant from a given point called the center

### Trigonometry and Relationships

Trigonometric Functions

Trigonometric functions can also be applied to circles, particularly when examining the unit circle

Reference Angles

Reference angles allow us to find the values of trigonometric functions for any angle by relating it to an acute angle with equivalent trigonometric function values

### Unit Circle

The unit circle is a powerful tool for visualizing and understanding the trigonometric functions

## Angles and Coordinate Plane

### Definition and Characteristics

An angle is formed by two rays with a common endpoint known as the vertex and is measured by the amount of rotation from one ray to the other

### Quadrants and Quadrantal Angles

Cartesian Coordinate Plane

The Cartesian coordinate plane is divided into four quadrants by the x and y axes

Quadrantal Angles

Quadrantal angles occur at 0, 90, 180, and 270 degrees (or 0, \(\frac{\pi}{2}\), \(\pi\), and \(\frac{3\pi}{2}\) radians) and have special properties in trigonometry

### Special Angles and Graphical Behavior

Special Angles

Certain angles, including 0, 30, 45, 60, 90, 180, 270, and 360 degrees (or 0, \(\frac{\pi}{6}\), \(\frac{\pi}{4}\), \(\frac{\pi}{3}\), \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), and \(2\pi\) radians), are commonly used in trigonometry

Graphical Behavior

The graphs of the sine, cosine, and tangent functions illustrate their periodic and symmetrical nature, with specific intervals for maximum, minimum, or zero values