Cosine Calculator

Cosine is a trigonometric function that relates the ratio of the length of the adjacent side to the hypotenuse in a right-angled triangle. In a right triangle with one angle as the reference angle, the cosine of that angle is defined as the length of the adjacent side divided by the length of the hypotenuse.

Mathematically, the cosine function is denoted as "cos" and is defined as follows: cos(angle) = adjacent / hypotenuse

In a unit circle (a circle with a radius of 1), the cosine of an angle can also be defined as the x-coordinate of the point on the unit circle corresponding to that angle.

The cosine function has a range between -1 and 1. When the angle is 0 degrees or 0 radians, the cosine value is 1. At 90 degrees or π/2 radians, the cosine value is 0. As the angle increases, the cosine value decreases until it reaches -1 at 180 degrees or π radians. The pattern continues as the angle increases further.

The cosine function is periodic with a period of 360 degrees (or 2π radians), meaning that it repeats its values after every 360 degrees (or 2π radians). It is an essential mathematical function used in trigonometry, calculus, physics, engineering, and many other fields to model periodic phenomena and perform various calculations involving angles and waves.

The cosine formula, also known as the Law of Cosines, is a fundamental mathematical equation used to calculate the length of an unknown side or measure an unknown angle in a triangle. It relates the lengths of the sides of a triangle to the cosine of its angles.

In a triangle with sides a, b, and c, and angles A, B, and C respectively, the cosine formula can be written as:

c² = a² + b² - 2ab * cos(C)

or

a² = b² + c² - 2bc * cos(A)

or

b² = a² + c² - 2ac * cos(B)

The formula can be used to solve for any of the three variables: side lengths (a, b, c) or angle measures (A, B, C). It is important to note that the angles must be measured in radians or degrees depending on the calculator or software being used.

The cosine formula is a generalization of the Pythagorean theorem for non-right triangles and is particularly useful for solving triangles where the side lengths are known, but not all the angles are given.

By rearranging the formula and solving for the desired variable, you can find missing side lengths or angles in a triangle when certain information is provided.