Question

(50 POINTS PLEASE HELP) What is the frequency of the sinusoidal graph? (picture attached)

Answer 1

`f=(3)/(2\pi)\; \sf Hz`

Explanation:

To determine the frequency of a sinusoidal graph, we need to know its period.

The period (T) is the length of one complete cycle of the wave, so it is the horizontal distance between two consecutive points where the graph reaches the same value. The frequency (f) is the number of cycles (oscillations) per unit of time and is the inverse of the period, which can be expressed mathematically as:

`f = (1)/(T)`

From observation of the given graph, it appears that there are 3 periods within the interval [0, 2π]. Therefore, the period (T) of the graph is:

`T=(2\pi)/(3)`

Substitute this period (T) into the frequency equation:

`f = (1)/((2\pi)/(3))`

`f=(3)/(2\pi)\; \sf Hz`

Therefore, the frequency of this sinusoidal graph is 3/2π Hertz, which means it completes 3/2π cycles (oscillations) per second.