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📰 Solution: The cosine function oscillates between $ -1 $ and $ 1 $, so $ 5\cos\left(\frac{\pi}{6}x\right) $ ranges from $ -5 $ to $ 5 $. Adding 10 shifts the range to $ [5, 15] $. The range is $ \boxed{[5, 15]} $. 📰 Question: A historian of science examines a 17th-century manuscript describing trigonometric identities. Find $ \tan \left( \arccos \left( \frac{1}{\sqrt{2}} \right) \right) $, reflecting early geometric reasoning. 📰 Solution: Let $ \theta = \arccos\left(\frac{1}{\sqrt{2}}\right) $, so $ \cos \theta = \frac{1}{\sqrt{2}} $. Then $ \theta = 45^\circ $, and $ \tan \theta = 1 $. The answer is $ \boxed{1} $. 📰 Stella Violet 5529205 📰 The Lariat Necklace That Secures Every Outfitwith Instant Elegance 3976557 📰 Arielle Vandenberg 781605 📰 The Shocking Truth Hidden Inside The Estadio Olmpico Universitario 8824538 📰 Avatar Setup Roblox 1913646 📰 Linda Weston 7401431 📰 Step Up Your Game With The Hidden Mx Player Ios Icon Everyones Talking About 5890078 📰 What Companies Are In The Technology Field 4557119 📰 Donde Vives In English 3141111 📰 Washington Wizards Vs Portland Trail Blazers Match Player Stats 7794749 📰 From Rookie To Legend Him Ppg Fast Tracked To 500 Goals Heres How 1056526 📰 Hotel Amargosa Opera 8196239 📰 Unlock Game Changing Performance With The Gz Modifierstop Guessing Start Winning 3662654 📰 Aggergh The Stunning Annual Earnings Of The Us President You Need To Know 2375664 📰 Finally The Simplest Way To Sketch Beautiful Butterflies With Ease 3810333