Understanding and Evaluating the Tangent Function | Finding the Value of Tan 60°

tan 60°

The tangent function, denoted as tan, is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle to the angle of the triangle

The tangent function, denoted as tan, is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side of a right triangle to the angle of the triangle.

Tan 60° represents the tangent of the angle 60 degrees. To find the value of tan 60°, we need to refer to the unit circle or use a calculator.

On the unit circle, the angle 60 degrees corresponds to the point (√3/2, 1/2). The tangent is defined as the ratio of the y-coordinate (opposite side) to the x-coordinate (adjacent side) of that point.

So, for tan 60°, we have:

tan 60° = (opposite side) / (adjacent side) = (1/2) / (√3/2) = 1/√3, which can be further simplified by multiplying the numerator and denominator by √3:

tan 60° = (1/√3) * (√3/√3) = √3 / 3.

Therefore, the value of tan 60° is √3 / 3, which is an irrational number.

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