The apprximate value of `sin(31^(@))`, given that `1^(@)=0.0175, cos 30^(@)=0.8660` is

Options

A. `0.5100`
B. `0.5152`
C. `0.5295`
D. `0.5175`

Answer

B

Explanation

Let `f(x)=sinx`
`f'(x)=cosx`
`f(x+h)=sin(x+h)`
Let `a=30^(@),h=1`
`:.f(a+h)=f(a)+hf'(a)`
`impliesf(a+h)=sina+hcos a`
`impliesf(31)=sin 30^(@)+1.cos 30^(@)`
`implies f(31)=1/2+0.0175xx0.8660=0.51515`
`impliesf(31)=0.5152`