The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b 0$$ Determine the equation of the graph.
-For an electrical circuit, the voltage $\mathrm { E }$ is modeled by $\mathrm { E } = 2.7 \cos 28 \pi \mathrm { t }$, where $\mathrm { t }$ is the time in seconds. How many cycles are completed in one second?
A) 14 cycles
B) $2.7$ cycles
C) 28 cycles
D) $28 \pi$ cycles

Question

The function graphed is of the form y $$y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$$ Determine the equation of the graph.
-For an electrical circuit, the voltage $\mathrm { E }$ is modeled by $\mathrm { E } = 2.7 \cos 28 \pi \mathrm { t }$, where $\mathrm { t }$ is the time in seconds. How many cycles are completed in one second?
A) 14 cycles
B) $2.7$ cycles
C) 28 cycles
D) $28 \pi$ cycles

Quizplus · Accepted Answer

The equation given is $E = 2.7 \cos 28 \pi t$. The coefficient of $t$ inside the cosine function, $28\pi$, represents the angular frequency of the wave. To find the number of cycles completed in one second, we look at the coefficient of $t$ without the $\pi$, which is $28$. Since the period of the cosine function is $2\pi$, a coefficient of $28\pi$ means the function completes $28$ cycles in $2\pi$ seconds. However, since we are dealing with cycles per second, and the question directly relates to the coefficient $28\pi$ in terms of cycles per second, the correct interpretation is that the coefficient before $\pi$ directly indicates the number of cycles per second, leading to $14$ cycles per second, not $28$. This is because the frequency $f$ in cycles per second (Hz) is given by $f = \frac{\omega}{2\pi}$, where $\omega$ is the angular frequency in radians per second ($28\pi$ in this case). Therefore, $f = \frac{28\pi}{2\pi} = 14$ Hz, meaning $14$ cycles are completed in one second.

The Function Graphed Is of the Form Y y=asin⁡bx or y=acos⁡bx, where b>0y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0y=asinbx or y=acosbx, where b>0

The Function Graphed Is of the Form Y $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$