cos120

cos120 refers to the cosine of an angle measuring 120 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 angles beyond 90 degrees, the unit circle is often used to visualize trigonometric functions.

On the unit circle, an angle of 120 degrees is located in the second quadrant. This angle can be represented as 180 degrees minus 60 degrees, or as 90 degrees plus 30 degrees. Using these relationships, we can determine the exact value of cos120.

Specifically, cos120 is equal to -cos(180 - 120), which simplifies to -cos60. The value of cos60 is 1/2. Therefore, cos120 is -1/2. Alternatively, using the relationship with 90 degrees, cos120 is equal to -sin(120 - 90), which simplifies to -sin30. The value of sin30 is also 1/2. Thus, cos120 equals -1/2.

The value of cos120, which is -0.5, is a common value encountered in trigonometry and its applications in fields such as physics and engineering. It arises in calculations involving oscillations, wave phenomena, and rotational mechanics.