I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 3.5 : Derivatives of Trig Functions
12. The position of an object is given by \(s\left( t \right) = 2 + 7\cos \left( t \right)\) determine all the points where the object is not moving.
Show SolutionWe know that the object will not be moving if its velocity, which is simply the derivative of the position function, is zero. So, all we need to do is take the derivative, set it equal to zero and solve.
\[s'\left( t \right) = - 7\sin \left( t \right)\hspace{0.5in} \Rightarrow \hspace{0.5in} - 7\sin \left( t \right) = 0\]So, for this problem the object will not be moving anywhere that sine is zero. From our recollection of the unit circle we know that will be at,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{t = 0 + 2\pi n = 2\pi n\hspace{0.25in}{\mbox{and}}\hspace{0.25in}\,\,\,t = \pi + 2\pi n\hspace{0.25in}n = 0, \pm 1, \pm 2, \pm 3, \ldots }}\]