Question

Physical quantity x and y are related as $y=4tanx$ . If at $x=\frac{\pi }{4}$ radian error in measurement of $x$ is $2\%$ then find $\%$ error in measurement of $y$ at $x=\frac{\pi }{4}$ .

• A. $2\%$
• B. $\frac{\pi }{2}\%$
• C. $\frac{\pi }{6}\%$
• D. $\pi \%$

Answer 1

Answer: (B)

$\frac{dy}{dx}=4se{c}^{2}x,\frac{\Delta y}{y}=\frac{4se{c}^2\Delta x}{4tanx}$
$\frac{\Delta y}{y}\times 100=\frac{4se{c}^{2}x}{4tanx}\times \Delta x\times 100$
$=2\times \Delta x\times 100$
$\frac{\Delta x}{x}\times 100=2$
$100\Delta x=2\times \frac{\pi }{4}=\frac{\pi }{2}$
$\frac{\Delta y}{y}\times 100=\frac{\pi }{2}$