Solve sin7pi/16*cos5pi/18/sinfrac{11pi{9}*cos31pi/16}{7pia}

$$\frac { \sin \frac { 7 \pi } { 16 } \cdot \cos \frac { 5 \pi } { 18 } } { \sin \frac { 11 \pi } { 9 } \cdot \cos \frac { 31 \pi } { 16 } } { 7 \pi a }$$

Evaluate

$$-\frac{54106487476514634\pi a}{5845720306089695}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.7729498210930662}{-0.5845720306089695} {(7 \pi a)}$$

Expand \frac{0.7729498210930662}{-0.5845720306089695} by multiplying both numerator and the denominator by 10000000000000000.

$$\frac{7729498210930662}{-5845720306089695}\times 7\pi a$$

Fraction \frac{7729498210930662}{-5845720306089695} can be rewritten as -\frac{7729498210930662}{5845720306089695} by extracting the negative sign.

$$-\frac{7729498210930662}{5845720306089695}\times 7\pi a$$

Express -\frac{7729498210930662}{5845720306089695}\times 7 as a single fraction.

$$\frac{-7729498210930662\times 7}{5845720306089695}\pi a$$

Multiply -7729498210930662 and 7 to get -54106487476514634.

$$\frac{-54106487476514634}{5845720306089695}\pi a$$

Fraction \frac{-54106487476514634}{5845720306089695} can be rewritten as -\frac{54106487476514634}{5845720306089695} by extracting the negative sign.

$$-\frac{54106487476514634}{5845720306089695}\pi a$$

Differentiate w.r.t. a

$$-\frac{54106487476514634 \pi}{5845720306089695} = -29\frac{454654691165341}{5845720306089695} = -29.077775649083264$$