Solve cos285^circ-sin255/sin525^circ-sin105^circ

$$\frac { \cos 285 ^ { \circ } - \sin 255 } { \sin 525 ^ { \circ } - \sin 105 ^ { \circ } }$$

Evaluate

$$-\frac{122474487139158943}{70710678118654750}\approx -1.732050808$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.25881904510252113 - -0.9659258262890683}{0.2588190451025208 - 0.9659258262890683}$$

The opposite of -0.9659258262890683 is 0.9659258262890683.

$$\frac{0.25881904510252113+0.9659258262890683}{0.2588190451025208-0.9659258262890683}$$

Add 0.25881904510252113 and 0.9659258262890683 to get 1.22474487139158943.

$$\frac{1.22474487139158943}{0.2588190451025208-0.9659258262890683}$$

Subtract 0.9659258262890683 from 0.2588190451025208 to get -0.7071067811865475.

$$\frac{1.22474487139158943}{-0.7071067811865475}$$

Expand \frac{1.22474487139158943}{-0.7071067811865475} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{122474487139158943}{-70710678118654750}$$

Fraction \frac{122474487139158943}{-70710678118654750} can be rewritten as -\frac{122474487139158943}{70710678118654750} by extracting the negative sign.

$$-\frac{122474487139158943}{70710678118654750}$$

Factor

$$-\frac{122474487139158943}{70710678118654750} = -1\frac{51763809020504190}{70710678118654750} = -1.7320508075688779$$