Solve =(cospi/14+cos3pi/14)-(cos3pi/14+cos5pi/14)+(cosfrac{5pi}{14}

$$= ( \cos \frac { \pi } { 14 } + \cos \frac { 3 \pi } { 14 } ) - ( \cos \frac { 3 \pi } { 14 } + \cos \frac { 5 \pi } { 14 } ) + ( \cos \frac { 5 \pi } { 14 }$$

Evaluate

$$0.5410441730642654$$

Solution Steps

Evaluate trigonometric functions in the problem

$${(0.9749279121818236 + 0.7818314824680298)} - {(0.7818314824680298 + 0.4338837391175582)}$$

Add 0.9749279121818236 and 0.7818314824680298 to get 1.7567593946498534.

$$1.7567593946498534-\left(0.7818314824680298+0.4338837391175582\right)$$

Add 0.7818314824680298 and 0.4338837391175582 to get 1.215715221585588.

$$1.7567593946498534-1.215715221585588$$

Subtract 1.215715221585588 from 1.7567593946498534 to get 0.5410441730642654.

$$0.5410441730642654$$

Factor

$$\frac{38028181 \cdot 71137267}{2 ^ {15} \cdot 5 ^ {16}} = 0.5410441730642654$$