The sine function touches the x-axis at which x-values?

The sine function touches the x-axis at which x-values?

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

Answer: (C)

The sine curve crosses the x-axis where its value is zero, so we look for x such that sin x = 0. This happens when the angle is a multiple of π. In one complete cycle from 0 to 2π, the zeros occur at 0, π, and 2π. So the x-values where the graph touches the x-axis are 0, π, and 2π. (For reference, π/2 and 3π/2 are the peaks and troughs, where sine is 1 or -1, not zero.)

The sine curve crosses the x-axis where its value is zero, so we look for x such that sin x = 0. This happens when the angle is a multiple of π. In one complete cycle from 0 to 2π, the zeros occur at 0, π, and 2π. So the x-values where the graph touches the x-axis are 0, π, and 2π. (For reference, π/2 and 3π/2 are the peaks and troughs, where sine is 1 or -1, not zero.)