Solve sin(30^circ)/cos(45^circ)

$$\frac { \sin ( 30 ^ { \circ } ) } { \cos ( 45 ^ { \circ } ) }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Solution Steps

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

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

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

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2 in both numerator and denominator.

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