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📰 Question: A mammalogist observes that the social cohesion index $ S $ of a primate group over time is modeled by $ S = \left| \sin\left(\frac{3\pi}{7} t\right) + \cos\left(\frac{4\pi}{7} t\right) \right| $, where $ t $ is time in days. How many times in one full cycle of $ S $ (i.e., over $ t \in [0, 7) $) does $ S = 1 $? 📰 Solution: The function $ S(t) = \left| \sin\left(\frac{3\pi}{7} t\right) + \cos\left(\frac{4\pi}{7} t\right) \right| $ has period $ T $, where both components repeat. The fundamental period is the least common multiple of the periods of $ \sin\left(\frac{3\pi}{7} t\right) $ and $ \cos\left(\frac{4\pi}{7} t\right) $. 📰 The angular frequencies are $ \frac{3\pi}{7} $ and $ \frac{4\pi}{7} $, so periods are $ \frac{2\pi}{3\pi/7} = \frac{14}{3} $, and $ \frac{2\pi}{4\pi/7} = \frac{7}{2} $. The LCM of $ \frac{14}{3} $ and $ \frac{7}{2} $ is found by expressing as rational multiples. 📰 The Ultimate Guide To Xurs Hidden Locationeverything Revealed Youre Missing 6511202 📰 Superman Story You Never Knew Villains Bringing The Ultimate Showdown 5438593 📰 Selco Credit Union Hacks Save Big On Mortgages Loans With These Hidden Tools 1104110 📰 Arjuna And 5804901 📰 Intern At Oracle 5413902 📰 The Shocking Secret Behind Invesco Qqq That No One Talks About 6109324 📰 Zuzu Nashville 3970039 📰 Horoscope For December 22Nd 8987558 📰 How To Change Screen Resolution Instantlywatch Your Tech Feel New Today 9637541 📰 No More Messy Backyardsdiscover Edger For Lawn Perfection You Never Knew You Needed 3639537 📰 Free Amigurumi Patterns 6569420 📰 Epic Gameslogin 708194 📰 Raising Kanan Season 3 9489570 📰 Trouble Game Rules 7909310 📰 Core Temperature Software 9308856