Understanding the Tangent of π/6 in Trigonometry | Calculation and Explanation

tan π/6 (30)

The expression “tan π/6” refers to the tangent of the angle π/6 (30 degrees) in trigonometry

The expression “tan π/6” refers to the tangent of the angle π/6 (30 degrees) in trigonometry.

To find the value of tangent (tan) π/6, we can use the reference angle, which is the acute angle formed with the x-axis in the Cartesian coordinate system. The reference angle for π/6 is π/6 itself since it is less than π/2.

The tangent function (tan) is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. In this case, we consider a right triangle where the angle π/6 is formed.

The reference triangle for π/6 has one side of length 1 as the adjacent side and another side of length √3 as the opposite side. The hypotenuse of the triangle can be found using the Pythagorean theorem, which gives us √(1^2 + (√3)^2) = √4 = 2.

Now, we can calculate the tangent of π/6:

tan(π/6) = opposite/adjacent = (√3)/1 = √3

Therefore, the value of tan π/6 is √3 or approximately 1.732.

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