Solve 1.2/4left(1-sin(4.71)/4.71right)

$$\frac{ 1.2 }{ 4 } \left( 1- \frac{ \sin ( 4.71 ) }{ 4.71 } \right)$$

Evaluate

$$\frac{231394377329017629}{785000000000000000}\approx 0.294769907$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{1.2}{4} {(1 - \frac{0.08211245341964742}{4.71})}$$

Expand \frac{1.2}{4} by multiplying both numerator and the denominator by 10.

$$\frac{12}{40}\left(1-\frac{0.08211245341964742}{4.71}\right)$$

Reduce the fraction \frac{12}{40} to lowest terms by extracting and canceling out 4.

$$\frac{3}{10}\left(1-\frac{0.08211245341964742}{4.71}\right)$$

Expand \frac{0.08211245341964742}{4.71} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{3}{10}\left(1-\frac{8211245341964742}{471000000000000000}\right)$$

Reduce the fraction \frac{8211245341964742}{471000000000000000} to lowest terms by extracting and canceling out 6.

$$\frac{3}{10}\left(1-\frac{1368540890327457}{78500000000000000}\right)$$

Convert 1 to fraction \frac{78500000000000000}{78500000000000000}.

$$\frac{3}{10}\left(\frac{78500000000000000}{78500000000000000}-\frac{1368540890327457}{78500000000000000}\right)$$

Since \frac{78500000000000000}{78500000000000000} and \frac{1368540890327457}{78500000000000000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{10}\times \frac{78500000000000000-1368540890327457}{78500000000000000}$$

Subtract 1368540890327457 from 78500000000000000 to get 77131459109672543.

$$\frac{3}{10}\times \frac{77131459109672543}{78500000000000000}$$

Multiply \frac{3}{10} times \frac{77131459109672543}{78500000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 77131459109672543}{10\times 78500000000000000}$$

Do the multiplications in the fraction \frac{3\times 77131459109672543}{10\times 78500000000000000}.

$$\frac{231394377329017629}{785000000000000000}$$

Factor

$$\frac{3 \cdot 127 \cdot 607334323698209}{157 \cdot 2 ^ {15} \cdot 5 ^ {16}} = 0.2947699074255002$$