0 is an acute angle and sin0 is given. use the pythagorean indentity sin^2 0+cos^2 0=1 to find cos 0. sin0=1/4

Question

1. ^/[]15 over 4
2. ^/[]15 over 15
3. 4
4. 4^/[]15 over 15

Answer 1

If sin O = 1/4, then sin^2 O = 1/16
So 1/16+cos^2 O = 1
cos^2 O = 15/16
cos O sqrt(15)/4

Answer 2

It sure is confusing when you try to use 0 as a variable, but I'll play along.

cos^2(O) = 1 - sin^2(O)
cos(O) = ±√(1 - sin^2(O))
cos(O) = ±√(1 - (1/16))
cos(O) = ±√(15/16)
cos(O) = ±√(15)/4
But since O is acute, cos(O) is positive, so
cos(O) = √(15)/4

Answer 3

Sin^2O + Cos^2O = 1
CosO = Sqrt(1 -Sin^2O) = sqrt(1 - 1/16) =
CosO = Sqrt(15/16) = 0.9682