Solve.
-A rotating beacon is located a distance $\mathrm { d }$ from a long wall. The distance $\mathrm { d }$ is given by $\mathrm { d } = 8$ tan $2 \pi \mathrm { t }$, where $t$ is the time measured in seconds since the beacon started rotating. Solve the equation for $t$.
A) $t = \frac { 1 } { 2 \pi } \tan \frac { d } { 8 }$
B) $t = \frac { 1 } { 2 \pi } \arctan \frac { d } { 8 }$
C) $t = 2 \pi \tan \frac { d } { 8 }$
D) $t = 2 \pi \arctan \frac { d } { 8 }$

Question

Quizplus · Accepted Answer

To solve for $t$, we need to isolate $t$ on one side of the equation. Starting with $\mathrm { d } = 8 \tan(2 \pi \mathrm { t })$, we first divide both sides by 8, getting $\frac{\mathrm { d }}{8} = \tan(2 \pi \mathrm { t })$. Then, to solve for $t$, we take the inverse tangent (arctan) of both sides, resulting in $2 \pi \mathrm { t } = \arctan(\frac{\mathrm { d }}{8})$. Finally, dividing both sides by $2 \pi$ gives $t = \frac { 1 } { 2 \pi } \arctan \frac { d } { 8 }$.

Solve -A Rotating Beacon Is Located a Distance d\mathrm { d }d

Solve
-A Rotating Beacon Is Located a Distance $\mathrm { d }$