Solve tanpi/3/sinfrac{pi{4}}

$$\frac { \tan \frac { \pi } { 3 } } { \sin \frac { \pi } { 4 } }$$

Evaluate

$$\sqrt{6}\approx 2.449489743$$

Solution Steps

Get the value of \tan(\frac{\pi }{3}) from trigonometric values table.

$$\frac{\sqrt{3}}{\sin(\frac{\pi }{4})}$$

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

$$\frac{\sqrt{3}}{\frac{\sqrt{2}}{2}}$$

Divide \sqrt{3} by \frac{\sqrt{2}}{2} by multiplying \sqrt{3} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{\sqrt{3}\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{3}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{3}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{3}\times 2\sqrt{2}}{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{6}\times 2}{2}$$

Cancel out 2 and 2.

$$\sqrt{6}$$