Suppose the angle G is in the first quadrant 0 lessthanorequ

Suppose the angle G is in the first quadrant, 0 lessthanorequalto theta lessthanorequalto pi/2, and sin(theta) = 1/4. Find exact values (as fractions, not decimal approximations) for the following.

Solution

sin theta= 1/4

here opposite=1 and hypotenuse=4 therefore adjacent= sqrt(16-1)=sqrt 15

cos theta= adjacent/hypotenuse= sqrt15/4

csc theta= 1/sin theta= 4