Solve sinpi/2/sinfrac{pi{4}}

$$\frac { \sin \frac { \pi } { 2 } } { \sin \frac { \pi } { 4 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Get the value of \sin(\frac{\pi }{2}) from trigonometric values table.

$$\frac{1}{\sin(\frac{\pi }{4})}$$

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

$$\frac{1}{\frac{\sqrt{2}}{2}}$$

Divide 1 by \frac{\sqrt{2}}{2} by multiplying 1 by the reciprocal of \frac{\sqrt{2}}{2}.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 and 2.

$$\sqrt{2}$$