Calculating the Value of tan(π/6) and its Explanation

tan(π/6)

The expression tan(π/6) refers to the tangent of the angle π/6, which is equivalent to 30 degrees in degrees measure

The expression tan(π/6) refers to the tangent of the angle π/6, which is equivalent to 30 degrees in degrees measure. In order to find the value of tan(π/6), we can use the unit circle or reference angles.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane. Angles on the unit circle are measured in radians. To find the value of tan(π/6), we can look at the point where the terminal side of the angle intersects the unit circle.

For π/6, the terminal side intersects the unit circle at the point (√3/2, 1/2). The tangent of an angle is defined as the ratio of the length of the leg opposite the angle to the length of the leg adjacent to the angle in a right triangle.

In this case, the leg opposite the angle is 1/2 and the leg adjacent to the angle is √3/2. Therefore, the value of tan(π/6) can be calculated as:

tan(π/6) = (1/2) / (√3/2) = 1/√3 = √3/3

So, tan(π/6) is equal to √3/3 or approximately 0.577.

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