Question

Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]

Answer 1

Let f(x) = cos x
 f '(x) = - sin x

`x=89^@ 30'=(89(1/2))^@=pi/2-1^@/2=a+h`

`here a=pi/2 `

`and h=-1^@/2=-0.0175/2=-0.00875`

`f(a)=f(pi/2)=cos(pi/2)=0`

`f'(a)=f'(pi/2)=-sin(pi/2)=-1`

`f(a+h)~~f(a)+hf'(a)`

`cos(89^@30')~~0+(– 0.00875) (–1)`

`~~0.00875`