The equation of a particle executing a S.H.M. is given by `x =4 "sin" omega t+ 5 "cos" omega t`. The "tan"gent of the initial phase angle is given by

Options

A. `"tan" alpha =(2)/(3)`
B. `"tan" alpha =1`
C. `"tan" alpha =(5)/(4)`
D. `"tan" alpha= (4)/(5)`

Answer

C

Explanation

`x = A "sin" (omega t+ alpha)= A "sin" omega t "cos" alpha + A "cos" omega t "sin" alpha` comparing the equations we get
` A "cos" alpha =4 and A "sin" alpha =5`
`therefore "tan" alpha=(5)/(4)`