Solve 4/sin45^circ*sin60^circ

$$\frac { 4 } { \sin 45 ^ { \circ } } \times \sin 60 ^ { \circ }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

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

$$\frac{4}{\frac{\sqrt{2}}{2}}\sin(60)$$

Divide 4 by \frac{\sqrt{2}}{2} by multiplying 4 by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{4\times 2}{\sqrt{2}}\sin(60)$$

Rationalize the denominator of \frac{4\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\sin(60)$$

The square of \sqrt{2} is 2.

$$\frac{4\times 2\sqrt{2}}{2}\sin(60)$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{2}}{2}\sin(60)$$

Divide 8\sqrt{2} by 2 to get 4\sqrt{2}.

$$4\sqrt{2}\sin(60)$$

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

$$4\sqrt{2}\times \frac{\sqrt{3}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

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

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

$$2\sqrt{6}$$