Solve 3sin(195^circ)-2cos(165)/2sin(75)+cos(255)

$$\frac { 3 \sin ( 195 ^ { \circ } ) - 2 \cos ( 165 ) } { 2 \sin ( 75 ) + \cos ( 255 ) }$$

Evaluate

$$\frac{115539451727057535}{167303260747561597}\approx 0.690598923$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{3 \cdot -0.25881904510252035 - 2 \cdot -0.9659258262890682}{2 \cdot 0.9659258262890683 + -0.25881904510252063}$$

Multiply 3 and -0.25881904510252035 to get -0.77645713530756105.

$$\frac{-0.77645713530756105-2\left(-0.9659258262890682\right)}{2\times 0.9659258262890683-0.25881904510252063}$$

Multiply 2 and -0.9659258262890682 to get -1.9318516525781364.

$$\frac{-0.77645713530756105-\left(-1.9318516525781364\right)}{2\times 0.9659258262890683-0.25881904510252063}$$

The opposite of -1.9318516525781364 is 1.9318516525781364.

$$\frac{-0.77645713530756105+1.9318516525781364}{2\times 0.9659258262890683-0.25881904510252063}$$

Add -0.77645713530756105 and 1.9318516525781364 to get 1.15539451727057535.

$$\frac{1.15539451727057535}{2\times 0.9659258262890683-0.25881904510252063}$$

Multiply 2 and 0.9659258262890683 to get 1.9318516525781366.

$$\frac{1.15539451727057535}{1.9318516525781366-0.25881904510252063}$$

Subtract 0.25881904510252063 from 1.9318516525781366 to get 1.67303260747561597.

$$\frac{1.15539451727057535}{1.67303260747561597}$$

Expand \frac{1.15539451727057535}{1.67303260747561597} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{115539451727057535}{167303260747561597}$$

Factor

$$\frac{3 \cdot 5 \cdot 23 \cdot 8537 \cdot 39228881519}{317 \cdot 4723 \cdot 15601 \cdot 7162667} = 0.6905989232414975$$