The approximate value of sec 59^{circ} obtain | vedclass

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(C) Let $f(x) = \sec x$. Then $f^{\prime}(x) = \sec x 	an x$. We take $a = 60^{\circ}$ and $h = -1^{\circ} = -0.0174$ radians. At $a = 60^{\circ}$, $

Vedclass · Accepted Answer

$1.9397$

Vedclass · Answer

(C) Let $f(x) = \sec x$. Then $f^{\prime}(x) = \sec x 	an x$. We take $a = 60^{\circ}$ and $h = -1^{\circ} = -0.0174$ radians. At $a = 60^{\circ}$, $f(a) = \sec 60^{\circ} = 2$. Also, $f^{\prime}(a) = \sec 60^{\circ} 	an 60^{\circ} = 2 	imes \sqrt{3} = 2 	imes 1.732 = 3.464$. Using the linear approximation formula $f(a+h) \approx f(a) + h \cdot f^{\prime}(a)$: $f(59^{\circ}) \approx f(60^{\circ}) + (-0.0174) 	imes f^{\prime}(60^{\circ})$. $f(59^{\circ}) \approx 2 + (-0.0174) 	imes (3.464)$. $f(59^{\circ}) \approx 2 - 0.0602736$. $f(59^{\circ}) \approx 1.9397264$. Rounding to four decimal places, we get $1.9397$.

The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ} = 0.0174$ radians and $\sqrt{3} = 1.732$ is

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