Solve 441[22/7*60/360-1/2sin60]

$$441 [ \frac { 22 } { 7 } \times \frac { 60 } { 360 } - \frac { 1 } { 2 } \sin 60 ]$$

Evaluate

$$-\frac{441\sqrt{3}}{4}+231\approx 40.041398466$$

Short Solution Steps

Reduce the fraction \frac{60}{360} to lowest terms by extracting and canceling out 60.

$$441\left(\frac{22}{7}\times \frac{1}{6}-\frac{1}{2}\sin(60)\right)$$

Multiply \frac{22}{7} and \frac{1}{6} to get \frac{11}{21}.

$$441\left(\frac{11}{21}-\frac{1}{2}\sin(60)\right)$$

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

$$441\left(\frac{11}{21}-\frac{1}{2}\times \frac{\sqrt{3}}{2}\right)$$

Multiply \frac{1}{2} times \frac{\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.

$$441\left(\frac{11}{21}-\frac{\sqrt{3}}{2\times 2}\right)$$

Multiply 2 and 2 to get 4.

$$441\left(\frac{11}{21}-\frac{\sqrt{3}}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21 and 4 is 84. Multiply \frac{11}{21} times \frac{4}{4}. Multiply \frac{\sqrt{3}}{4} times \frac{21}{21}.

$$441\left(\frac{11\times 4}{84}-\frac{21\sqrt{3}}{84}\right)$$

Since \frac{11\times 4}{84} and \frac{21\sqrt{3}}{84} have the same denominator, subtract them by subtracting their numerators.

$$441\times \frac{11\times 4-21\sqrt{3}}{84}$$

Do the multiplications in 11\times 4-21\sqrt{3}.

$$441\times \frac{44-21\sqrt{3}}{84}$$

Express 441\times \frac{44-21\sqrt{3}}{84} as a single fraction.

$$\frac{441\left(44-21\sqrt{3}\right)}{84}$$

Use the distributive property to multiply 441 by 44-21\sqrt{3}.

$$\frac{19404-9261\sqrt{3}}{84}$$