The disperod of a particle varies according to the relation `x=4 (cos pit+ sinpit)`. The amplitude of the particle is.

Options

A. `-4`
B. 4
C. `4 sqrt2`
D. 8

Answer

C

Explanation

`x =4 ( cos pi t + sin pit )`
`= 4 sqrt2 ((1)/( sqrt2 ) cos pi t (1)/(sqrt2) sin pit )`
`= 4 sqrt2 [ sin ""( pi)/(4) cos pi t + cos "" (pi)/(t) sin pi t ]`
`= 4 sqrt2 [ sin pi t cos ""(pi)/(4) + cos pi t sin ""(pi)/(4)]`
`= 4 sqrt2 sin (pi t + (pi)/(4))`