if sin(theta)=1/4

Question

and pie/2<theta<pie what is the value of cos(theta)

Answer 1

make a rough sketch of a right-angled triangle in the second quadrant with a hypotenuse of 4 and a vertical leg of 1.
(remember sin(angle) = opposite/hypotenuse)

by Pythagoras, the other side must be √15

in the second quadrant the cosine is negative, so
cos(theta) = -√15/4