Find the approximate values of :
`cos(89^(@)30)," given "1^(@)=0.0175^( c )`.

Explanation

Let `f(x)=cos x`
`:.f'(x)=("d")/("dx")(cos x)=-sin x`
Take `a=90^(@)=(pi)/(2)` and
`h=-30=(-(1)/(2))^(@)=-((1)/(2)xx0.0175)^(c)=-0.00875^(c)`
Then `f(a)=f((pi)/(2))=cos""(pi)/(2)=0`
`f'(a)=f'((pi)/(2))=-sin""(pi)/(2)=-1`
The formula for approximation is
`f(a+h)=f(a)+h.f'(a)`
`:.cos(89^(@)30)=f(89^(@)30)=f((pi)/(2)-0.00875)`
`=f((pi)/(2))-0.00875.f'((pi)/(2))`
`=0-0.00875(-1)=0.00875`
`:. cos (89^(@)30)=0.00875`.