Determine the frequency of y = 2 �� 3 cos 10x. (nearest tenth)
Please help!
I cannot determine your function, and in fact, I do not see time as a variable.
For y = sin(wx) or y = cos(wx), w = 2pi*f (where f is frequency). So f = w/(2pi).
For y = 3cos(10x), f = 10/(2pi) = 5/pi.
To determine the frequency of the given function y = 2αcos(βx), where α represents the amplitude and β represents the frequency, we need to find the value of β.
In this case, the given function is y = 2 �� 3 cos 10x, which means α = 3 and β = 10.
The frequency (denoted as f) is the reciprocal of the period (T) of the function. The period is the length of one complete cycle of the function.
For a cosine function, the period (T) is calculated by dividing 2π by the absolute value of β. So, in this case, T = 2π / |10| = π/5.
Since the frequency (f) is the reciprocal of the period, we can calculate it by taking the reciprocal of the value of T: f = 1 / (π/5).
To find the answer, we need to evaluate the expression f = 1 / (π/5) and round it to the nearest tenth.
Calculating f:
f = 1 / (π/5)
f = 5 / π
Now, we can approximate the value of f by dividing 5 by the value of π. Rounding to the nearest tenth, we get:
f ≈ 5 / π ≈ 1.59 (nearest tenth)
Therefore, the frequency of the given function y = 2 �� 3 cos 10x is approximately 1.6 (nearest tenth).