If `theta` and `phi` are acute angles satisfying `sin theta=1/2, cos phi=1/3` then `theta+phi=`

Options

A. `(pi//3,pi//2]`
B. `(pi//2,2pi//3]`
C. `(2pi//3,5pi//6]`
D. `(5pi//6,pi]`

Answer

B

Explanation

We have,
`sin theta=1/2and cos phi=1/3`
`impliescostheta=(sqrt3)/(2)and sin phi=(2sqrt2)/(3)`
Now, `sin(theta+phi)=sinthetacosphi+costhetasinphi`
`sin(theta+phi)=1/6+sqrt((2)/(3))=0.1.66+0.816=0.982`
`impliestheta+phi"is in hte neighbourhood of"(pi)/(2).`
Also, `sintheta=1/2impliestheta=(pi)/(6)and, cosphi=1/3implies(pi)/(3)ltphilt(pi)/(2)`
`thereforetheta+phigt(pi)/(2).`
Hence, `theta+phiin((pi)/(2),(2pi)/(3)]`