Answer:
Explanation:
The period of the function y = sin(x/4) is calculated by finding the length of one complete cycle of the graph. In this case, the period is determined by the coefficient in front of x, which is 4.
To find the period, we can use the formula T = 2π/|b|, where T represents the period and b is the coefficient in front of x.
In the given function, the coefficient is 4, so we substitute it into the formula:
T = 2π/|4| = 2π/4 = π/2
Therefore, the period of y = sin(x/4) is π/2. This means that the graph of the function completes one full cycle every π/2 units.
For example, if we look at the values of x between 0 and π/2, we can observe that the graph of y = sin(x/4) starts at 0, reaches its maximum at π/2, and then returns to 0.
Remember, the period of a function represents the distance it takes for the function to repeat itself. In this case, the graph repeats itself every π/2 units.