What Is the Name of COS? Simple Answer Explained

The cosine function, often written as cos, is one of the three primary trigonometric functions. If you are asking “what is the name of cos” in the sense of its formal mathematical name, the answer is cosine. It is a standard function used to relate the angles of a right triangle to the ratio of the adjacent side and the hypotenuse.

What Cosine Means

Cosine is defined for a given angle in a right triangle as the length of the side adjacent to that angle divided by the length of the hypotenuse. In a unit circle (a circle with a radius of 1), the cosine of an angle gives the x-coordinate of the point where the terminal side of the angle meets the circle.

Quick example: For a 60-degree angle in a right triangle, the cosine is 0.5. This means the adjacent side is half the length of the hypotenuse. If the hypotenuse is 10 units, the adjacent side is 5 units.

The function is periodic, meaning it repeats its values in regular intervals. Cosine has a period of 360 degrees (or 2π radians). It is an even function, so cos(θ) = cos(-θ). Cosine values range from -1 to 1.

Cosine in the Unit Circle

The unit circle definition extends cosine beyond right triangles to all angles, including those greater than 90 degrees or negative angles. Place a circle centered at the origin with radius 1. For any angle measured counterclockwise from the positive x-axis, the point where the angle’s ray meets the circle has coordinates (cos θ, sin θ). So cos θ is simply the x-coordinate of that point.

For a 120-degree angle, the terminal side lands in the second quadrant. The x-coordinate there is negative: cos 120° = -0.5. This matches the right-triangle definition if you consider the reference angle of 60 degrees, but the sign flips because the adjacent side points left.

Key Takeaways

• The name of the cos function is cosine.
• Cosine equals the adjacent side divided by the hypotenuse in a right triangle.
• On the unit circle, cosine represents the x-coordinate of an angle’s terminal point.
• Cosine values repeat every 360 degrees (2π radians) and stay between -1 and 1.