Tan390s

Tan390s refers to a specific numerical value. In trigonometry, the tangent function, denoted as 'tan', is a fundamental trigonometric function. The input '390s' indicates an angle measured in degrees. Therefore, tan390s represents the tangent of an angle of 390 degrees.

The tangent function is periodic with a period of 180 degrees, meaning that tan(θ) = tan(θ + n * 180°) for any integer n. To evaluate tan390s, we can subtract multiples of 180° to find an equivalent angle within a standard range, such as 0° to 180°. Subtracting 180° twice from 390° gives 390° - 360° = 30°. Thus, tan390s is equivalent to tan30s.

The tangent of 30 degrees is a well-known value in trigonometry. It can be calculated using the ratio of the opposite side to the adjacent side in a right-angled triangle with angles 30°, 60°, and 90°. For a 30-60-90 triangle, the sides are in the ratio 1 : √3 : 2. At 30°, the opposite side is 1 and the adjacent side is √3. Therefore, tan30s = 1/√3, which can also be rationalized to √3/3.

In summary, tan390s is a trigonometric value equal to the tangent of 390 degrees. Due to the periodicity of the tangent function, this is equivalent to tan30s, which has a numerical value of 1/√3 or √3/3.

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