Question

The approximate value of $\tan {46}^o$ is (take $\pi =22/7$) :

• A. $3$
• B. $1.035$
• C. $1.033$
• D. $1.135$

Answer 1

The correct option is B $1.035$

Let$y=f\left(x\right)=tanx;x=45or\left(\frac{\pi }{4}\right)$and$x+\Delta x=46$

Then,$\Delta x=1=\left(0.01745\right)c$

For$x=\frac{\pi }{4}$,we have

$y=f\left(\frac{\pi }{4}\right)=tan\left(\frac{\pi }{4}\right)=1$

Let$dx=\Delta x=0.01745$

$y=tanx\Rightarrow \frac{dy}{dx}={sec}^{2}x\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\frac{\pi }{4}}\Rightarrow {sec}^2\frac{\pi }{4}=2$

Therefore,$dy=\frac{dy}{dx}\ast dx\Rightarrow dy=2\times \left(0.01745\right)=0.03490$

$\Delta y=0.03490[\Delta y\cong dy]$

Hence,$tan46=y+\Delta y=1+0.03490=1.035$