If the graph y = 4sin(bt) repeats itself every 30 degrees (and not more frequently), find the
value of b.
To find the value of b, we need to consider the period of the graph. The period represents the distance between two consecutive repetitions or cycles of a function.
In the given equation, y = 4sin(bt), the general form of a sine function is y = A*sin(Bt), where A represents the amplitude and B represents the frequency (or the number of cycles in a given interval).
Since the graph repeats itself every 30 degrees, we can convert it to radians, as sine functions are typically measured in radians. 30 degrees is equivalent to π/6 radians.
The standard formula for the period of a sine function is T = 2π/B.
So, in this case, T = π/6 radians. Now we can solve for B:
T = 2π/B
π/6 = 2π/B
To find B, we can cross-multiply and solve for it:
B*(π/6) = 2π
B = (2π) / (π/6)
Simplifying further:
B = (2π) * (6/π)
B = 12
Therefore, the value of b in the equation y = 4sin(bt) is 12.