A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain peroidic motion :
(a) `y = asin2pi t//T`
(b) y=asinvt
`("c")` `y=(a//T) sin t//a`
(d) `y=(a//sqrt2) (sin 2pi t//T + cos 2pit//T)`
(a = maximum displacement of the particle, v=speed of the particle. T=time-period of motion). Rule out the wrong formulas on dimensional grounds)

Explanation

(b)and `("c")` are wrong on dimensional grounds. Hint, The argument of a trignometric function must almost must always be dimensionless.