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.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 5.6 \cos 40 \pi \mathrm { t }$, where $t$ is time measured in seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one second).
A) $\frac { 1 } { 40 }$
B) $\frac { 1 } { 20 }$
C) 40
D) 20

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.
-The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 5.6 \cos 40 \pi \mathrm { t }$, where $t$ is time measured in seconds. Find the frequency of the function (that is, find the number of cycles or periods completed in one second).
A) $\frac { 1 } { 40 }$
B) $\frac { 1 } { 20 }$
C) 40
D) 20

Quizplus · Accepted Answer

The frequency $f$ of a function given by $E = a \cos(bx)$ or $E = a \sin(bx)$ is calculated as $f = \frac{b}{2\pi}$. For the given function $E = 5.6 \cos(40\pi t)$, $b = 40\pi$, so the frequency is $f = \frac{40\pi}{2\pi} = 20$.

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 $y = a \sin b x \text { or } y = a \cos b x , \text { where } b > 0$