Solve 18-(cos60^circ)div2^-1-4sqrt{sin30^circ}-12

$$18 - ( \cos 60 ^ { \circ } ) \div 2 ^ { - 1 } - 4 \sqrt { \sin 30 ^ { \circ } } - 12$$

Evaluate

$$5-2\sqrt{2}\approx 2.171572875$$

Solution Steps

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

$$18-\frac{\frac{1}{2}}{2^{-1}}-4\sqrt{\sin(30)}-12$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$18-\frac{\frac{1}{2}}{\frac{1}{2}}-4\sqrt{\sin(30)}-12$$

Divide \frac{1}{2} by \frac{1}{2} to get 1.

$$18-1-4\sqrt{\sin(30)}-12$$

Subtract 1 from 18 to get 17.

$$17-4\sqrt{\sin(30)}-12$$

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

$$17-4\sqrt{\frac{1}{2}}-12$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$17-4\times \frac{\sqrt{1}}{\sqrt{2}}-12$$

Calculate the square root of 1 and get 1.

$$17-4\times \frac{1}{\sqrt{2}}-12$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$17-4\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-12$$

The square of \sqrt{2} is 2.

$$17-4\times \frac{\sqrt{2}}{2}-12$$

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

$$17-2\sqrt{2}-12$$

Subtract 12 from 17 to get 5.

$$5-2\sqrt{2}$$