Solve E/sin(frac{pi{4})}

$$\frac { E } { \sin ( \frac { \pi } { 4 } ) }$$

Evaluate

$$\sqrt{2}E$$

Solution Steps

Get the value of \sin(\frac{\pi }{4}) from trigonometric values table.

$$\frac{E}{\frac{\sqrt{2}}{2}}$$

Divide E by \frac{\sqrt{2}}{2} by multiplying E by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{E\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{E\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{E\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{E\times 2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$E\sqrt{2}$$

Differentiate w.r.t. E

$$\sqrt{2} = 1.414213562$$