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# Solution for Using Differential, Find the Approximate Value of the Sin ( 22 14 ) ? - CBSE (Science) Class 12 - Mathematics

#### Question

Using differential, find the approximate value of the $\sin\left( \frac{22}{14} \right)$ ?

#### Solution

$\text { Consider the function } y = f\left( x \right) = \sin x .$

$\text { Let }:$

$x = \frac{22}{7}$

$x + ∆ x = \frac{22}{14}$

$\text { Then,}$

$∆ x = \frac{- 22}{14}$

$\text { For } x = \pi,$

$y = \sin \left( \frac{22}{7} \right) = 0$

$\text { Let }:$

$dx = ∆ x = \sin \frac{- 22}{14} = - \sin \left( \frac{\pi}{2} \right) = - 1$

$\text { Now }, y = \sin x$

$\Rightarrow \frac{dy}{dx} = \cos x$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = \frac{22}{7}} = - 1$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = - 1 \times \left( - 1 \right) = 1$

$\Rightarrow ∆ y = 1$

$\therefore \sin \frac{22}{14} = y + ∆ y = 1$

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Solution for question: Using Differential, Find the Approximate Value of the Sin ( 22 14 ) ? concept: Approximations. For the courses CBSE (Science), CBSE (Commerce), CBSE (Arts), PUC Karnataka Science
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