The approximate value of cos(30^{circ} 30^{pr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $f(x) = \cos x$. Then $f^{\prime}(x) = -\sin x$. We need to find the value of $\cos(30^{\circ} 30^{\prime})$. Here,$30^{\circ} 30^{\prime} = 3

Vedclass · Accepted Answer

$0.8616$

Vedclass · Answer

(D) Let $f(x) = \cos x$. Then $f^{\prime}(x) = -\sin x$. We need to find the value of $\cos(30^{\circ} 30^{\prime})$. Here,$30^{\circ} 30^{\prime} = 30^{\circ} + 30^{\prime} = 30^{\circ} + (0.5)^{\circ}$. Converting $0.5^{\circ}$ to radians: $0.5 	imes 0.0175 = 0.00875 	ext{ rad}$. Let $a = 30^{\circ} = \frac{\pi}{6} 	ext{ rad}$ and $h = 0.00875 	ext{ rad}$. Using the linear approximation formula $f(a+h) \approx f(a) + h f^{\prime}(a)$: $f(a+h) \approx \cos(30^{\circ}) + (0.00875)(-\sin(30^{\circ}))$. Given $\cos 30^{\circ} = 0.8660$ and $\sin 30^{\circ} = 0.5$. $f(a+h) \approx 0.8660 - 0.00875 	imes 0.5$. $f(a+h) \approx 0.8660 - 0.004375 = 0.861625$. Rounding to four decimal places,we get $0.8616$.

The approximate value of $\cos(30^{\circ} 30^{\prime})$ is,given that $1^{\circ} = 0.0175 \text{ rad}$ and $\cos 30^{\circ} = 0.8660$.

Similar Questions

If there is an error of $\pm 0.04 \text{ cm}$ in the measurement of the diameter of a sphere,then the approximate percentage error in its volume,when the radius is $10 \text{ cm}$,is

The approximate value of the function $f(x) = x^{3} + 5x^{2} - 7x + 10$ at $x = 1.1$ is (in $.6$)

If the area of a square is $575$ square units,then the approximate value of its side is

Find the approximate value of $(81.5)^{\frac{1}{4}}$.

If $1^{\circ} = \alpha$ radians,then the approximate value of $\cos(60^{\circ} 1^{\prime})$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module