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# Solution for Using Differential, Find the Approximate Value of the Cos ( 11 π 36 ) ? - CBSE (Commerce) Class 12 - Mathematics

#### Question

Using differential, find the approximate value of the $\cos\left( \frac{11\pi}{36} \right)$ ?

#### Solution

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

$\text { Let }:$

$x = \frac{\pi}{3}$

$x + ∆ x = \frac{11\pi}{36}$

$\text { Then,}$

$∆ x = \frac{- \pi}{36} = - 5^\circ$

$\text { For } x = \frac{\pi}{3},$

$y = \cos \left( \frac{\pi}{3} \right) = 0 . 5$

$\text { Let }:$

$dx = ∆ x = - \sin 5^\circ = - 0 . 08716$

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

$\Rightarrow \frac{dy}{dx} = - \sin x$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = \frac{\pi}{3}} = - 0 . 86603$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = - 0 . 86603 \times \left( - 0 . 08716 \right) = 0 . 075575$

$\Rightarrow ∆ y = 0 . 075575$

$\therefore \cos\frac{11\pi}{36} = y + ∆ y = 0 . 5 + 0 . 075575 = 0 . 575575$

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Solution Using Differential, Find the Approximate Value of the Cos ( 11 π 36 ) ? Concept: Approximations.
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