Solve frac{sin56^{circ}*sin124^{circ}-sin34^{circ}*cos236^circ}{cos28^circ*cos88^circ+cos178^circ*sin208}

$$\frac { \sin 56 ^ { \circ } \cdot \sin 124 ^ { \circ } - \sin 34 ^ { \circ } \cdot \cos 236 ^ { \circ } } { \cos 28 ^ { \circ } \cdot \cos 88 ^ { \circ } + \cos 178 ^ { \circ } \cdot \sin 208 }$$

Evaluate

$$\frac{105026137398336590}{111191426364934869}\approx 0.944552479$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{0.7244859782065077 - -0.3257753957768582}{0.9998545651113364 + 0.11205969853801229}$$

The opposite of -0.3257753957768582 is 0.3257753957768582.

$$\frac{0.7244859782065077+0.3257753957768582}{0.9998545651113364+0.11205969853801229}$$

Add 0.7244859782065077 and 0.3257753957768582 to get 1.0502613739833659.

$$\frac{1.0502613739833659}{0.9998545651113364+0.11205969853801229}$$

Add 0.9998545651113364 and 0.11205969853801229 to get 1.11191426364934869.

$$\frac{1.0502613739833659}{1.11191426364934869}$$

Expand \frac{1.0502613739833659}{1.11191426364934869} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{105026137398336590}{111191426364934869}$$

Factor

$$\frac{2 \cdot 5 \cdot 10502613739833659}{3 \cdot 71 \cdot 149 \cdot 3503526683837} = 0.9445524788362412$$