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