Solve 2/sin45^circ=

$$\frac { 2 } { \sin 45 ^ { \circ } } =$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

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

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 2 and 2 to get 4.

$$\frac{4\sqrt{2}}{2}$$

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

$$2\sqrt{2}$$