Løs 15+10cos19-13cos26/10sin19+13sin26

$$\frac { 15 + 10 \cos 19 - 13 \cos 26 } { 10 \sin 19 + 13 \sin 26 }$$

Evaluer

$$\frac{63854315770519985}{44772532264147863}\approx 1,426193975$$

Løsningsvejledning

Evaluate trigonometric functions in the problem

$$\frac{15 + 10 \cdot 0,9455185755993168 - 13 \cdot 0,898794046299167}{10 \cdot 0,32556815445715664 + 13 \cdot 0,4383711467890774}$$

Multiplicer 10 og 0,9455185755993168 for at få 9,455185755993168.

$$\frac{15+9,455185755993168-13\times 0,898794046299167}{10\times 0,32556815445715664+13\times 0,4383711467890774}$$

Tilføj 15 og 9,455185755993168 for at få 24,455185755993168.

$$\frac{24,455185755993168-13\times 0,898794046299167}{10\times 0,32556815445715664+13\times 0,4383711467890774}$$

Multiplicer 13 og 0,898794046299167 for at få 11,684322601889171.

$$\frac{24,455185755993168-11,684322601889171}{10\times 0,32556815445715664+13\times 0,4383711467890774}$$

Subtraher 11,684322601889171 fra 24,455185755993168 for at få 12,770863154103997.

$$\frac{12,770863154103997}{10\times 0,32556815445715664+13\times 0,4383711467890774}$$

Multiplicer 10 og 0,32556815445715664 for at få 3,2556815445715664.

$$\frac{12,770863154103997}{3,2556815445715664+13\times 0,4383711467890774}$$

Multiplicer 13 og 0,4383711467890774 for at få 5,6988249082580062.

$$\frac{12,770863154103997}{3,2556815445715664+5,6988249082580062}$$

Tilføj 3,2556815445715664 og 5,6988249082580062 for at få 8,9545064528295726.

$$\frac{12,770863154103997}{8,9545064528295726}$$

Udvid \frac{12,770863154103997}{8,9545064528295726} ved at gange både tælleren og nævneren med 10000000000000000.

$$\frac{127708631541039970}{89545064528295726}$$

Reducer fraktionen \frac{127708631541039970}{89545064528295726} til de laveste led ved at udtrække og annullere 2.

$$\frac{63854315770519985}{44772532264147863}$$

Faktoriser

$$\frac{5 \cdot 19 \cdot 331 \cdot 2030666744173}{3 \cdot 7 \cdot 1979 \cdot 2267 \cdot 475220371} = 1\frac{19081783506372120}{44772532264147864} = 1,4261939752210997$$