Trig equation

Question

0

54

1

+1926

Let $\theta$ be an acute angle. If $\cos \theta = \frac{3}{11},$ then what is $\sin \theta?$

tomtom Oct 28, 2023

parmen · Answer 1 · 2023-10-28T08:17:39

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.