Solve sin(2pi/12)/cos(frac{7pi{12})}

$$\frac { \sin ( \frac { 2 \pi } { 12 } ) } { \cos ( \frac { 7 \pi } { 12 } ) }$$

Evaluate

$$-\frac{50000000000000000}{25881904510252063}\approx -1.931851653$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{\sin(\frac{2 \pi}{12})}{-0.25881904510252063}$$

Divide 2\pi by 12 to get \frac{1}{6}\pi .

$$\frac{\sin(\frac{1}{6}\pi )}{-0.25881904510252063}$$

Get the value of \sin(\frac{1}{6}\pi ) from trigonometric values table.

$$\frac{\frac{1}{2}}{-0.25881904510252063}$$

Express \frac{\frac{1}{2}}{-0.25881904510252063} as a single fraction.

$$\frac{1}{2\left(-0.25881904510252063\right)}$$

Multiply 2 and -0.25881904510252063 to get -0.51763809020504126.

$$\frac{1}{-0.51763809020504126}$$

Expand \frac{1}{-0.51763809020504126} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{100000000000000000}{-51763809020504126}$$

Reduce the fraction \frac{100000000000000000}{-51763809020504126} to lowest terms by extracting and canceling out 2.

$$-\frac{50000000000000000}{25881904510252063}$$

Factor

$$-\frac{50000000000000000}{25881904510252063} = -1\frac{24118095489747936}{25881904510252064} = -1.9318516525781375$$