Cosine function touches the x-axis at which x-values?

Cosine function touches the x-axis at which x-values?

• A. 0 and 2pi
• B. pi and 2pi
• C. 0 and pi
• D. pi/2 and 3pi/2

Answer: (D)

The value where the cosine function crosses the x-axis is where cos x = 0. In one full cycle from 0 to 2π, those x-values are π/2 and 3π/2. At these angles the point on the unit circle lies on the y-axis, so the x-coordinate (which is cos x) is zero. The other numbers don’t give zero because cos 0 = 1, cos π = −1, and cos 2π = 1. Since cosine repeats every 2π, the zeros occur again at π/2 + kπ for any integer k.

The value where the cosine function crosses the x-axis is where cos x = 0. In one full cycle from 0 to 2π, those x-values are π/2 and 3π/2. At these angles the point on the unit circle lies on the y-axis, so the x-coordinate (which is cos x) is zero. The other numbers don’t give zero because cos 0 = 1, cos π = −1, and cos 2π = 1. Since cosine repeats every 2π, the zeros occur again at π/2 + kπ for any integer k.