tan18

tan18 refers to the trigonometric function tangent evaluated at an angle of 18 degrees. The value of tan18 is an irrational number, approximately 0.3249. This specific trigonometric value can be derived using algebraic methods, often involving the properties of regular pentagons or the angle subtraction formulas. While not as commonly memorized as values like tan30 or tan45, tan18 arises in various geometric calculations, particularly those involving pentagonal symmetry. It is also related to other trigonometric values, for example, tan18 = sin36 / cos36. The precise algebraic expression for tan18 is (√(5 - 2√5)) / (√5 + 1). Understanding and calculating tan18 can be useful in fields such as physics, engineering, and advanced geometry where precise angular relationships are important.