Question

Displacement of a particle is given by y=ashinbx+csindt
where x is distance and t is time .
Find the dimension of constant

Answer 1

The sine or cosine argument quantities should be dimentionless. Thus, if the dimentions of time is seconds ($[t] = s$) then the dimentions of $b$ and $d$ are:

$$[b] = [d] = \dfrac{1}{s}$$

Again, the result of sine or cosine is dimentionless. Thus, if the dimention of distance is meter, then:

$$[a] = [c] = m$$

Answer. The dimentions of $a$ and $c$ are meters. The dimentions of $b$ and $d$ are $s^{-1}$.