tan12

tan12 refers to the trigonometric function tangent evaluated at an angle of 12 degrees. The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side. Mathematically, tan(θ) = opposite/adjacent.

The value of tan12 degrees is an irrational number, meaning it cannot be expressed as a simple fraction of two integers. Its approximate decimal value is 0.21255656167. This value can be calculated using trigonometric tables, a calculator, or through more complex mathematical derivations involving trigonometric identities.

In trigonometry, tan12 degrees can be expressed in terms of radicals using the half-angle or angle subtraction formulas. For instance, using the tangent half-angle formula, tan(θ/2) = ±√((1-cos θ)/(1+cos θ)), and knowing the value of cos24 degrees, one could derive an expression for tan12. Alternatively, using the angle subtraction formula for tangent, tan(A-B) = (tanA - tanB) / (1 + tanA tanB), one could compute tan12 by using values like tan30 degrees and tan18 degrees.

The value of tan12 degrees finds applications in various fields, including engineering, physics, and geometry, where calculations involving specific angles are necessary. It is a component in solving problems related to slopes, heights, and distances in surveying, navigation, and construction.