Solve sin(30)cos(45)/tan(60)

$$\frac{ \sin ( 30 ) \cos ( 45 ) }{ \tan ( 60 ) }$$

Evaluate

$$\frac{\sqrt{6}}{12}\approx 0.204124145$$

Solution Steps

Get the value of \sin(30) from trigonometric values table.

$$\frac{\frac{1}{2}\cos(45)}{\tan(60)}$$

Get the value of \cos(45) from trigonometric values table.

$$\frac{\frac{1}{2}\times \frac{\sqrt{2}}{2}}{\tan(60)}$$

Multiply \frac{1}{2} times \frac{\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\sqrt{2}}{2\times 2}}{\tan(60)}$$

Get the value of \tan(60) from trigonometric values table.

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

Express \frac{\frac{\sqrt{2}}{2\times 2}}{\sqrt{3}} as a single fraction.

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

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

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

The square of \sqrt{3} is 3.

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

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

$$\frac{\sqrt{6}}{2\times 2\times 3}$$

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{6}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{\sqrt{6}}{12}$$