Riješi frac{5cos0^{circ}-2sin30^{circ}+sqrt{3}cos30^{circ}}{tan30^{circ}*tan60^circ*cos60^circ}+3sin29^circsec61^circ

$$\frac { 5 \cos 0 ^ { \circ } - 2 \sin 30 ^ { \circ } + \sqrt { 3 } \cos 30 ^ { \circ } } { \tan 30 ^ { \circ } \times \tan 60 ^ { \circ } \times \cos 60 ^ { \circ } } + 3 \sin 29 ^ { \circ } \sec 61 ^ { \circ }$$

Izračunaj

$$\frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}\approx 20,636230939$$

Kratki koraci za rješenje

Evaluate trigonometric functions in the problem

$$\frac{5 \cos(0) - 2 \sin(30) + \sqrt{3} \cos(30)}{0,3118580165482944} + 3 \cdot 0,48480962024633706 \cdot 2,062665339627314$$

Nabavite vrijednost \cos(0) iz tablice trigonometrijskih vrijednosti.

$$\frac{5\times 1-2\sin(30)+\sqrt{3}\cos(30)}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Pomnožite 5 i 1 da biste dobili 5.

$$\frac{5-2\sin(30)+\sqrt{3}\cos(30)}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Nabavite vrijednost \sin(30) iz tablice trigonometrijskih vrijednosti.

$$\frac{5-2\times \frac{1}{2}+\sqrt{3}\cos(30)}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Pomnožite 2 i \frac{1}{2} da biste dobili 1.

$$\frac{5-1+\sqrt{3}\cos(30)}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Oduzmite 1 od 5 da biste dobili 4.

$$\frac{4+\sqrt{3}\cos(30)}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Nabavite vrijednost \cos(30) iz tablice trigonometrijskih vrijednosti.

$$\frac{4+\sqrt{3}\times \frac{\sqrt{3}}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Izrazite \sqrt{3}\times \frac{\sqrt{3}}{2} kao jedan razlomak.

$$\frac{4+\frac{\sqrt{3}\sqrt{3}}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Pomnožite 4 i \frac{2}{2}.

$$\frac{\frac{4\times 2}{2}+\frac{\sqrt{3}\sqrt{3}}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Budući da \frac{4\times 2}{2} i \frac{\sqrt{3}\sqrt{3}}{2} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{\frac{4\times 2+\sqrt{3}\sqrt{3}}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Pomnožite izraz 4\times 2+\sqrt{3}\sqrt{3}.

$$\frac{\frac{8+3}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Izračunajte izraz 8+3.

$$\frac{\frac{11}{2}}{0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Izrazite \frac{\frac{11}{2}}{0,3118580165482944} kao jedan razlomak.

$$\frac{11}{2\times 0,3118580165482944}+3\times 0,48480962024633706\times 2,062665339627314$$

Pomnožite 2 i 0,3118580165482944 da biste dobili 0,6237160330965888.

$$\frac{11}{0,6237160330965888}+3\times 0,48480962024633706\times 2,062665339627314$$

Proširite \frac{11}{0,6237160330965888} tako da i brojnik i nazivnik pomnožite sa 10000000000000000.

$$\frac{110000000000000000}{6237160330965888}+3\times 0,48480962024633706\times 2,062665339627314$$

Skratite razlomak \frac{110000000000000000}{6237160330965888} na najmanje vrijednosti tako da izlučite i poništite 128.

$$\frac{859375000000000}{48727815085671}+3\times 0,48480962024633706\times 2,062665339627314$$

Pomnožite 3 i 0,48480962024633706 da biste dobili 1,45442886073901118.

$$\frac{859375000000000}{48727815085671}+1,45442886073901118\times 2,062665339627314$$

Pomnožite 1,45442886073901118 i 2,062665339627314 da biste dobili 2,99999999999999987246512207937052.

$$\frac{859375000000000}{48727815085671}+2,99999999999999987246512207937052$$

Dodajte \frac{859375000000000}{48727815085671} broju 2,99999999999999987246512207937052 da biste dobili \frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}.

$$\frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}$$