Solve 115-978*sin5^circ/978*cos5^circ

$$\frac { 115 - 978 \cdot \sin 5 ^ { \circ } } { 978 \cdot \cos 5 ^ { \circ } }$$

Evaluate

$$\frac{1488084179639515487}{48713920736686354950}\approx 0.030547411$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{115 - 978 \cdot 0.08715574274765817}{978 \cdot 0.9961946980917455}$$

Multiply 978 and 0.08715574274765817 to get 85.23831640720969026.

$$\frac{115-85.23831640720969026}{978\times 0.9961946980917455}$$

Subtract 85.23831640720969026 from 115 to get 29.76168359279030974.

$$\frac{29.76168359279030974}{978\times 0.9961946980917455}$$

Multiply 978 and 0.9961946980917455 to get 974.278414733727099.

$$\frac{29.76168359279030974}{974.278414733727099}$$

Expand \frac{29.76168359279030974}{974.278414733727099} by multiplying both numerator and the denominator by 100000000000000000.

$$\frac{2976168359279030974}{97427841473372709900}$$

Reduce the fraction \frac{2976168359279030974}{97427841473372709900} to lowest terms by extracting and canceling out 2.

$$\frac{1488084179639515487}{48713920736686354950}$$

Factor

$$\frac{17099213 \cdot 87026471899}{2 \cdot 3 \cdot 163 \cdot 271 \cdot 499 \cdot 12503 \cdot 1178393 \cdot 5 ^ {2}} = 0.030547411440829522$$