sin theta=4/7, find the exact value of sin (theta+Pie/6)

Answer 1

Use the sin(A + B) formula

sin(A + B) = sin A cosB + sin B cosA,
where A = sin^-1(4/7) and B = pi/6

sin(pi/6) = 1/2
cos(pi/6)= (sqrt3)/2
sin(theta) = 4/7 = 0.57143
cos(theta) = sqrt[1 - (4/7)^2]
= sqrt(33/49) = 0.82065

Take it from there.