In the study of trigonometry, a key aspect is understanding the graphical representation of trigonometric functions. This section focuses on the sine, cosine, and tangent functions, which are integral in many areas of mathematics and physics.

**Basic Definitions**

**Sine Function**$( \sin )$: For an angle $\theta$, sine is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle.

**Cosine Function**$( \cos )$: Cosine of $\theta$ is the ratio of the adjacent side to the hypotenuse.

**Tangent Function**$( \tan )$: Tangent is the ratio of the opposite side to the adjacent side.

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**Characteristics of Trigonometric Graphs**

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**Sine and Cosine Graphs**

**Amplitude**: The peak height from the midline of the graph.**Period**: The length of one complete cycle of the wave, typically $2\pi$radians (360 degrees).**Phase Shift**: The horizontal shift of the graph; positive shift indicates a move to the right.**Vertical Shift**: The upward or downward displacement of the graph.

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**Tangent Graph**

**Asymptotes**: The tangent graph has repeating vertical asymptotes and no defined amplitude or period.

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