For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0.
$d = \frac { 1 } { 64 } \sin 794 \pi t$
A) $64$
B) $\frac { 1 } { 794 }$
C) $794$
D) $\frac { 1 } { 64 }$
E) $\frac { 1 } { 1,584 }$

Question

For the simple harmonic motion described by the trigonometric function, find the least positive value of t for which d = 0.  
  $d = \frac { 1 } { 64 } \sin 794 \pi t$  
A) $64$
B) $\frac { 1 } { 794 }$
C) $794$  
D) $\frac { 1 } { 64 }$  
E) $\frac { 1 } { 1,584 }$

Quizplus · Accepted Answer

For $d = \frac{1}{64} \sin 794\pi t$ to be zero, the argument of the sine function, $794\pi t$, must be an integer multiple of $\pi$. The least positive value of $t$ that satisfies this condition is when the multiple is 1, so $794\pi t = \pi$, which simplifies to $t = \frac{1}{794}$.

For the Simple Harmonic Motion Described by the Trigonometric Function d=164sin⁡794πtd = \frac { 1 } { 64 } \sin 794 \pi td=641​sin794πt

For the Simple Harmonic Motion Described by the Trigonometric Function $d = \frac { 1 } { 64 } \sin 794 \pi t$