The general equation of a wave travelling along negative x-axis

y=Asin(kx+wt+phi)

given T of the wave=25 millisecond

i.e. w=2(pi)/T

=2(pi)/25(10^-3)

=(2000)(pi)/25=80(pi)

Further,

given for x=0 n t=0

y=0.02m

i.e. Asin(phi)=0.02........(1)

Further, particle velocity is specified

i.e.Awcos(phi)=-2.........(2)

so, you can find tan(phi) by dividing (1) by (2)

hence the phase angle can also be found.

For the first, use the value of phi in one of the equations for the answer.

Your mistake is that in the first section, you have assumed the particle at x=0 and t=0 to have a phase 0, i.e. you assumed that phi=0, hence the error.

In the second part the discrepancy is because you got the

**Principal Solution of the equation.**
Since trigonometric functions are periodic, the value of sin1.2 and sin 1.95 are the same

.

The appropriate value is decided by the value of the cosine of the phi angle, which is negative [from (2)]

and since the cosine of an obtuse angle is negative, the phi is obtuse and 1.95 and not 1.2