hello, what is the cos(t) if sin(t) = Radical seven over 6

Sin(t) =Sqrt(7) / 6 =0.44095855

0.44095855^2 + cos(t)^2 =1

0.19444 + cos(t)^2 =1

Cos(t) =Sqrt(1 - 0.19444) =0.80556

Cos(t) = Sqrt(0.80556)

Cos(t) =0.897527....

Imagine a right angled triangle with hypotenuse of length 6 and opposite side to angle t of length sqrt(7).  Then the adjacent length is sqrt(6^2 - sqrt(7)^2) or sqrt(36 - 7) or sqrt(29).  Hence cos(t) = sqrt(29)/6

 

.