cos30circ

cos30circ refers to the cosine of an angle measuring 30 degrees. In trigonometry, the cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. For an angle of 30 degrees, this ratio has a specific, well-defined value.

The value of cos30circ is commonly expressed as the square root of 3 divided by 2. This can be written mathematically as $\frac{\sqrt{3}}{2}$. This exact value is derived from the properties of a 30-60-90 right triangle, which is a special type of triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. In such a triangle, the sides are in a specific ratio: if the side opposite the 30-degree angle has length x, then the side opposite the 60-degree angle has length $x\sqrt{3}$, and the hypotenuse has length 2x. Applying the cosine definition to the 30-degree angle (adjacent side $x\sqrt{3}$ and hypotenuse 2x) yields $\frac{x\sqrt{3}}{2x} = \frac{\sqrt{3}}{2}$.

Numerically, $\frac{\sqrt{3}}{2}$ is approximately equal to 0.866025. This value is frequently encountered in various fields of science and engineering, particularly in problems involving rotations, wave phenomena, and geometric calculations where 30-degree angles are involved. Its exact form is often preferred in mathematical contexts to avoid rounding errors.