Question

Physical quantity x and y are related as $y=4 \, tanx$ . 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)

$\frac{d y}{d x}=4s e c^{2}x, \, \, \, \frac{\Delta y}{y}=\frac{4 s e c^{2} \Delta x}{4t a n x}$
$\frac{\Delta y}{y}\times 100=\frac{4 s e c^{2} x}{4 t a n x}\times \Delta x\times 100$
$=2\times \Delta x\times 100$
$\frac{\Delta x}{x}\times 100=2$
$100 \, \Delta x=2\times \frac{\pi }{4}=\frac{\pi }{2}$
$\frac{\Delta y}{y}\times 100=\frac{\pi }{2}$