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Sin (sine) and cos (cosine) are fundamental trigonometric functions that play a crucial role in mathematics, physics, engineering, and various other fields. These functions are defined based on the ratios of the sides of a right triangle and are used to establish relationships between angles and side lengths. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Mathematically, sin(θ) = opposite/hypotenuse. The cosine of an angle, on the other hand, is the ratio of the length of the adjacent side to the length of the hypotenuse. This is represented as cos(θ) = adjacent/hypotenuse. Sin and cos functions are periodic, with a period of 2π (360 degrees). They exhibit specific properties such as being bounded between -1 and 1, and their values can be determined using trigonometric tables, calculators, or computational tools. These functions are used extensively in solving problems related to triangles,