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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. 📰 Best Free Games In Pc 📰 Amazon Prime Membership Rate 6648964 📰 Only One Moment Defines Everything Who Was There First 7047212 📰 Streetfoodfinder 📰 Post Malones New Song With Oreo Flavors Has Fans Breaking Down Inside 53177 📰 Reaper Program 📰 The Ultimate Guide To Shota Hentai Unraveled Shocking Fan Theories And Behind The Scenes Facts 2657055 📰 Red Dead Redemption Undead Horses 📰 Zelda Ocarina Of Time 6843015 📰 Star Sign For January 19Th 6610061 📰 The Secret Secrets Of Lord Mahadev That Every Devotee Must Know 1054836 📰 Haricots Verts From Farm To Table This Secret Ingredient Will Blow Your Mind 3659838 📰 Amc Riverview 14 2864093 📰 Friendship Movie Review 📰 Time For Care