What Is Cosine?

How cosine reads the triangle

Cosine stays the same for all similar right triangles with the same acute angle, which is why a ratio from one triangle can be used as a stable function value.

This page keeps the angle mark, the adjacent side, and the hypotenuse visible together so cosine is read from the triangle itself before it becomes symbolic notation.

For a 60-degree angle in a 30-60-90 triangle, the adjacent leg is half the hypotenuse, so cosine is one half. If the reference angle changes, the side called adjacent may change too. Naming the angle first prevents the ratio from being assembled backward.

Cosine is often useful when a problem gives a horizontal reach and a diagonal distance. The adjacent leg supplies the near direction, while the hypotenuse supplies the full slanted distance. The ratio compares those two lengths for one chosen angle.

• Cosine is the ratio of adjacent side to hypotenuse in a right triangle.
• Cosine is commonly remembered with CAH: adjacent over hypotenuse.
• The adjacent side depends on the chosen angle, so it changes if the reference angle changes.
• Cosine is closely related to sine through the same right-triangle structure, but it uses a different leg of the triangle.

Where cosine helps

• Use cosine when a right-triangle problem involves the adjacent side and the hypotenuse relative to a chosen angle.
• Use it in geometry and trigonometry problems involving horizontal distance, components, or side-length solving.
• Use cosine inside the SOH CAH TOA framework when selecting the correct ratio from given information.

Cosine checks to make

• Do not confuse the adjacent side with the opposite side; both depend on the marked angle.
• Do not use the hypotenuse as the adjacent side even though it touches the angle.
• Do not switch angles halfway through a problem and keep the same side labels.