Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 3 \cos 5 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. When does the weight first reach its maximum height?
A) After $\frac { 1 } { 5 } \mathrm { sec }$
B) After $\frac { 5 } { \pi } \sec$
C) After $\frac { \pi } { 5 } \sec$
D) After $\frac { 5 } { 4 } \mathrm { sec }$

Question

Quizplus · Accepted Answer

The weight reaches its maximum height when the cosine function equals 1, which occurs at the beginning of its cycle. Given the equation $s(t) = -3\cos(5\pi t)$, the period of the cosine function is $\frac{2\pi}{5\pi} = \frac{2}{5}$ seconds. The first maximum after $t = 0$ occurs at a quarter of the period, which is $\frac{1}{4} \times \frac{2}{5} = \frac{1}{5}$ seconds.

Determine the Equation of the Graph s(t)=−3cos⁡5πt\mathrm { s } ( \mathrm { t } ) = - 3 \cos 5 \pi \mathrm { t }s(t)=−3cos5πt

Determine the Equation of the Graph $\mathrm { s } ( \mathrm { t } ) = - 3 \cos 5 \pi \mathrm { t }$