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 position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 8 \cos 20 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?
A) The maximum height of 8 inches is first reached after $0.05$ seconds.
B) The maximum height of 16 inches is first reached after 5 seconds.
C) The maximum height of 8 inches is first reached after 10 seconds.
D) The maximum height of 16 inches is first reached after 10 seconds.

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 position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 8 \cos 20 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?
A) The maximum height of 8 inches is first reached after $0.05$ seconds.
B) The maximum height of 16 inches is first reached after 5 seconds.
C) The maximum height of 8 inches is first reached after 10 seconds.
D) The maximum height of 16 inches is first reached after 10 seconds.

Quizplus · Accepted Answer

The maximum height is determined by the amplitude of the cosine function, which is 8 inches in this case. The first maximum occurs at $t = \frac{1}{4} \times \frac{1}{20} = 0.05$ seconds, considering the period of the cosine function is $\frac{2\pi}{b}$, where $b = 20\pi$.

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