Let $\theta$ be an acute angle. If $\cos \theta = \frac{3}{11},$ then what is $\sin \theta?$
By the Pythagorean identity, we have sin2i+cos2i=1. Substitutingcosi=113,we getsin2i+(113)2=1,sosin2i=12196.
Taking the square root of both sides, we get sini=±1196. Sinceiis acute,sini must be positive. Therefore, sini=1196.
+1911 
