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

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

Arvuta

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

Lühike lahenduskäik

Evaluate trigonometric functions in the problem

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

Leidke \cos(0) väärtus trigonomeetriliste väärtuste tabelist.

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

Korrutage 5 ja 1, et leida 5.

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

Leidke \sin(30) väärtus trigonomeetriliste väärtuste tabelist.

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

Korrutage 2 ja \frac{1}{2}, et leida 1.

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

Lahutage 1 väärtusest 5, et leida 4.

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

Leidke \cos(30) väärtus trigonomeetriliste väärtuste tabelist.

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

Avaldage \sqrt{3}\times \frac{\sqrt{3}}{2} ühe murdarvuna.

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

Avaldiste liitmiseks või lahutamiseks laiendage need, et neil oleksid ühised nimetajad. Korrutage omavahel 4 ja \frac{2}{2}.

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

Kuna murdudel \frac{4\times 2}{2} ja \frac{\sqrt{3}\sqrt{3}}{2} on sama nimetaja, liitke nende lugejad.

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

Tehke korrutustehted võrrandis 4\times 2+\sqrt{3}\sqrt{3}.

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

Tehke arvutustehted avaldises 8+3.

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

Avaldage \frac{\frac{11}{2}}{0,3118580165482944} ühe murdarvuna.

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

Korrutage 2 ja 0,3118580165482944, et leida 0,6237160330965888.

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

Saate \frac{11}{0,6237160330965888} laiendada, korrutades nii lugeja kui ka nimetaja 10000000000000000.

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

Taandage murd \frac{110000000000000000}{6237160330965888} vähimale ühiskordsele, eraldades ja taandades arvu 128.

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

Korrutage 3 ja 0,48480962024633706, et leida 1,45442886073901118.

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

Korrutage 1,45442886073901118 ja 2,062665339627314, et leida 2,99999999999999987246512207937052.

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

Liitke \frac{859375000000000}{48727815085671} ja 2,99999999999999987246512207937052, et leida \frac{25138961131425324844637601292748537216888795473}{1218195377141775000000000000000000000000000000}.

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