The approximate value of cos 31^{circ} is (Ta | vedclass

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(D) Let $y = f(x) = \cos(x)$. We want to find the value of $\cos(31^{\circ})$.Let $x = 30^{\circ} = \frac{\pi}{6} 	ext{ rad}$ and $\Delta x = 1^{\cir

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$0.8573$

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(D) Let $y = f(x) = \cos(x)$. We want to find the value of $\cos(31^{\circ})$.Let $x = 30^{\circ} = \frac{\pi}{6} 	ext{ rad}$ and $\Delta x = 1^{\circ} = 0.0174 	ext{ rad}$.Then $f(x) = \cos(30^{\circ}) = \frac{\sqrt{3}}{2} \approx 0.8660$.The derivative is $f'(x) = -\sin(x)$.At $x = 30^{\circ}$,$f'(30^{\circ}) = -\sin(30^{\circ}) = -0.5$.Using the differential approximation $\Delta y \approx f'(x) \cdot \Delta x$:$\Delta y \approx (-0.5) 	imes 0.0174 = -0.0087$.Therefore,$\cos(31^{\circ}) = f(x + \Delta x) \approx f(x) + \Delta y$.$\cos(31^{\circ}) \approx 0.8660 - 0.0087 = 0.8573$.

The approximate value of $\cos 31^{\circ}$ is (Take $1^{\circ} = 0.0174 \text{ rad}$)

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