Question

Which of the following is the graph of y = sin(0.5x)? On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 24 pi. On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 2 pi. On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 1 cycle at 8 pi. On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. it goes through 2 cycles at 8 pi.

Answer 1

The graph of y = sin(0.5x) will have a period of 4π, meaning it completes one cycle every 4π units along the x-axis and goes through 2 cycles at 8π. It also oscillates between -1 and +1, and crosses the y-axis at (0, 0).

Step-by-step explanation:

The graph of the function y = sin(0.5x) represents a sine wave on a coordinate plane. Since a standard sine function y = sin(x) has a period of 2π radians, we need to understand how the coefficient 0.5 affects the period of our given sine wave. The period of a sine wave with the equation y = sin(kx) is calculated as 2π/k. So, for the function y = sin(0.5x), the period would be 2π/0.5 = 4π. This means that the sine wave completes one full cycle every 4π units along the x-axis. Therefore, it would go through 2 cycles at 8π, not at 2π, 24π, or 8pi. The correct graph should also oscillate between -1 and +1 and cross the y-axis at (0, 0).

Answer 2

The graph of y=sin(0.5x) is D

Step-by-step explanation: