Math for AI: A Guide | Built In
Math for AI: A Guide | Built In
Jan 19, 2024
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Features of sinusoidal functions
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Features of sinusoidal functions
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Triangular functions are a group of periodic mathematical functions that model repeating patterns found in both nature and engineering. They are closely related to trigonometric functions like sine and cosine, but instead of being smooth and curved, triangular functions form straight-line segments that rise and fall linearly, creating a sawtooth-like or “triangular” wave shape. A basic triangular wave increases linearly from a minimum to a maximum value and then decreases back to the minimum, re
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The functions sin θ and sin 2θ are both periodic trigonometric functions, but they differ significantly in frequency and behavior. Sin θ completes one full oscillation over an interval of 2π, while sin 2θ completes two full oscillations in the same interval, meaning it has double the frequency. This makes sin 2θ oscillate faster, with more peaks and troughs compared to sin θ. Additionally, while both functions have the same amplitude and range—from –1 to 1—their zero crossings and turning points
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Sine and cosine are two key functions in trigonometry that relate angles to the ratios of sides in a right triangle. In the context of the unit circle, the cosine of an angle gives the horizontal coordinate, while the sine gives the vertical coordinate of a point on the circle. These functions are periodic, meaning they repeat in a regular pattern every full rotation, or 360 degrees. Sine starts at zero and goes up and down in a wave-like motion, while cosine starts at one and follows a similar
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Sine and cosine are two of the most fundamental functions in mathematics, especially in trigonometry. They describe the relationship between the angles and sides of right triangles, but their importance extends far beyond geometry. The sine function gives the ratio of the length of the side opposite an angle to the hypotenuse, while the cosine function gives the ratio of the adjacent side to the hypotenuse. On the unit circle, sine corresponds to the y-coordinate of a point determined by an angl
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