Question

If $1$ degree $=0.017$ radians, then the approximate value of $\sin 46$ degrees is

• A. $0.7194$
• B. $\frac{0.017}{\sqrt{2}}$
• C. $\frac{1.017}{\sqrt{2}}$
• D. none of these

Answer 1

Answer: (C)

$\frac{1.017}{\sqrt{2}}$

$\sin {46}^0=\sin ({45}^0+1^0)$
Let $y=f\left(x\right)=\sin x$
$y+\Delta y=\sin (x+\Delta x)$
$\Rightarrow \Delta y=\sin (x+\Delta x)-\sin x$
Also, $\Delta y=f^{\prime }\left(x\right)\Delta x$
$\Rightarrow \sin (x+\Delta x)-\sin x=\cos x\Delta x$
Put $x={45}^0,\Delta x=1^0$
$\Rightarrow \sin {46}^0-\sin {45}^0=\cos {45}^0\left(1^0\right)$
$\Rightarrow \sin {46}^0=\frac{1.017}{\sqrt{2}}$