Solve the Equation for Exact Solutions $\mathrm { d }$ From a Long Wall

Solve the equation for exact solutions.
-A rotating beacon is located a distance $\mathrm { d }$ from a long wall. The distance $\mathrm { d }$ is given by $\mathrm { d } = 2 \tan 2 \pi \mathrm { t }$
where $t$ is the time measured in seconds since the beacon started rotating. Solve the equation for $t$ .

A) $\mathrm { t } = \frac { 1 } { 2 \pi } \arctan \frac { \mathrm { d } } { 2 }$
B) $\mathrm { t } = 2 \pi \tan \frac { \mathrm { d } } { 2 }$
C) $\mathrm { t } = 2 \pi \arctan \frac { \mathrm { d } } { 2 }$
D) $\mathrm { t } = \frac { 1 } { 2 \pi } \tan \frac { \mathrm { d } } { 2 }$

Correct Answer:

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