Which statement correctly describes the cosine function?

Which statement correctly describes the cosine function?

• A. It has a period of 360 degrees or 2π radians and cos 0 = 1
• B. It has a period of 180 degrees
• C. It starts at the origin
• D. It is always increasing

Answer: (A)

Cosine is a periodic function that repeats after a full rotation, so its period is 360 degrees or 2π radians. At x = 0, cos 0 equals 1, which is the maximum value the cosine curve attains. That combination—period 360 degrees (or 2π) and cos 0 = 1—captures how the cosine function behaves across its cycle. The other statements don’t fit: a period of 180 degrees would not reproduce the same values for all x, starting at the origin would require cos 0 to be 0, and the cosine function is not always increasing—it decreases from 1 to -1 in the first half of a cycle and then increases.

Cosine is a periodic function that repeats after a full rotation, so its period is 360 degrees or 2π radians. At x = 0, cos 0 equals 1, which is the maximum value the cosine curve attains. That combination—period 360 degrees (or 2π) and cos 0 = 1—captures how the cosine function behaves across its cycle. The other statements don’t fit: a period of 180 degrees would not reproduce the same values for all x, starting at the origin would require cos 0 to be 0, and the cosine function is not always increasing—it decreases from 1 to -1 in the first half of a cycle and then increases.