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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