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📰 Solution: The sine of $ \theta $ equals $ \frac{\sqrt{3}}{2} $ at $ 60^\circ $ and $ 120^\circ $ in the interval $ [0^\circ, 360^\circ] $. These angles correspond to the reference angle $ 60^\circ $ in the first and second quadrants. Thus, the solutions are $ \boxed{60^\circ} $ and $ \boxed{120^\circ} $. 📰 Question: A museum curator studying a 19th-century celestial sphere needs to determine the angle between two star positions modeled by vectors $ \begin{pmatrix} 2 \\ -1 \end{pmatrix} $ and $ \begin{pmatrix} x \\ 3 \end{pmatrix} $, which are orthogonal. Find $ x $. 📰 Solution: For vectors to be orthogonal, their dot product must be zero: $ 2x + (-1)(3) = 0 $. Solving $ 2x - 3 = 0 $ gives $ x = \frac{3}{2} $. The ordered pair is $ \boxed{\left( \frac{3}{2}, 3 \right)} $. 📰 You Wont Believe What Lilya Sliver Did After The Silence Ended 8927543 📰 Discover The Most Irresistible Burger Drawing That Will Make You Crave Flow 1241743 📰 House You Never Dreamed About Looks Impossible But Exists Inside Upside Down 4649163 📰 Wire Transfer Receipt Bank Of America 7676349 📰 Unlock The Ultimate Power In Pokmon Gaia No One Taught You Exist 7367851 📰 The Gardens Hotel Key West 6598151 📰 The House On Mango Street 9747803 📰 Arhat 9936145 📰 Best Crypto App 3981877 📰 How Many Planets In There 2104834 📰 Master Java String Splitting In Minutesthis Technique Will Save You Time 3861495 📰 What Has Alexander Skarsgard Been In 2753295 📰 The Long Awaited Payoff Arrivesvolume Ten Delivers Fire And Fury 3478766 📰 Excel Hack Remove Duplicate Rows Instantly Boost Productivity 4047519 📰 The Golden Corral Breakfast That Will Change How You Start Your Day Forever 6404278