sin(4*x)=sqrt(3)*sin(2*x)

Дано

$$\sin{\left (4 x \right )} = \sqrt{3} \sin{\left (2 x \right )}$$
Ответ
$$x_{1} = 0$$

-pi
x2 = —-
2

$$x_{2} = — \frac{\pi}{2}$$

pi
x3 = —
2

$$x_{3} = \frac{\pi}{2}$$

x4 = pi

$$x_{4} = \pi$$

/ / ___________________________________________________________________________________\ / ___ ___
| | / ___________ ___________ ___________ ___________ || | / 6 / 2 |
| | / / ___ ___ / ___ / ___ ___ / ___ || |- —— + ——|
|log(2) | / / / 3 — I / 3 */ / 3 — I I*/ / 3 — I I*/ 3 */ / 3 — I || | 4 4 |
x5 = pi + I*|—— — log| / ————— + ——————— — —————- + ———————- || + atan|—————|
2 \/ 2 2 2 2 // | ___ ___ |
| / 2 / 6 |
| —— + —— |
4 4 /

$$x_{5} = {atan}{\left (\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right )} + \pi + i \left(\frac{1}{2} \log{\left (2 \right )} — \log{\left (\sqrt{- \frac{i}{2} \sqrt{\sqrt{3} — i} + \frac{\sqrt{3}}{2} \sqrt{\sqrt{3} — i} + \frac{1}{2} \sqrt{\sqrt{3} — i} + \frac{\sqrt{3} i}{2} \sqrt{\sqrt{3} — i}} \right )}\right)$$

/ / ___________________________________________________________________________________\ / ___ ___
| | / ___________ ___________ ___________ ___________ || | / 6 / 2 |
| | / / ___ ___ / ___ / ___ ___ / ___ || |- —— + ——|
|log(2) | / / / 3 — I / 3 */ / 3 — I I*/ / 3 — I I*/ 3 */ / 3 — I || | 4 4 |
x6 = I*|—— — log| / ————— + ——————— — —————- + ———————- || + atan|—————|
2 \/ 2 2 2 2 // | ___ ___ |
| / 2 / 6 |
| —— + —— |
4 4 /

$$x_{6} = {atan}{\left (\frac{- \frac{\sqrt{6}}{4} + \frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right )} + i \left(\frac{1}{2} \log{\left (2 \right )} — \log{\left (\sqrt{- \frac{i}{2} \sqrt{\sqrt{3} — i} + \frac{\sqrt{3}}{2} \sqrt{\sqrt{3} — i} + \frac{1}{2} \sqrt{\sqrt{3} — i} + \frac{\sqrt{3} i}{2} \sqrt{\sqrt{3} — i}} \right )}\right)$$
Читайте также  -(1/4)*x+(4/5)=(13/10)

/ / ___________________________________________________________________________________\ / ___ ___
| | / ___________ ___________ ___________ ___________ || | / 2 / 6 |
| | / / ___ / ___ ___ / ___ ___ / ___ || |- —— + ——|
|log(2) | / / I + / 3 I*/ I + / 3 / 3 */ I + / 3 I*/ 3 */ I + / 3 || | 4 4 |
x7 = -pi + I*|—— — log| / ————— + —————- + ——————— — ———————- || + atan|—————|
2 \/ 2 2 2 2 // | ___ ___ |
| / 2 / 6 |
| —— + —— |
4 4 /

$$x_{7} = — \pi + {atan}{\left (\frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right )} + i \left(\frac{1}{2} \log{\left (2 \right )} — \log{\left (\sqrt{- \frac{\sqrt{3} i}{2} \sqrt{\sqrt{3} + i} + \frac{1}{2} \sqrt{\sqrt{3} + i} + \frac{\sqrt{3}}{2} \sqrt{\sqrt{3} + i} + \frac{i}{2} \sqrt{\sqrt{3} + i}} \right )}\right)$$

/ / ___________________________________________________________________________________\ / ___ ___
| | / ___________ ___________ ___________ ___________ || | / 2 / 6 |
| | / / ___ / ___ ___ / ___ ___ / ___ || |- —— + ——|
|log(2) | / / I + / 3 I*/ I + / 3 / 3 */ I + / 3 I*/ 3 */ I + / 3 || | 4 4 |
x8 = I*|—— — log| / ————— + —————- + ——————— — ———————- || + atan|—————|
2 \/ 2 2 2 2 // | ___ ___ |
| / 2 / 6 |
| —— + —— |
4 4 /

$$x_{8} = {atan}{\left (\frac{- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}}{\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}} \right )} + i \left(\frac{1}{2} \log{\left (2 \right )} — \log{\left (\sqrt{- \frac{\sqrt{3} i}{2} \sqrt{\sqrt{3} + i} + \frac{1}{2} \sqrt{\sqrt{3} + i} + \frac{\sqrt{3}}{2} \sqrt{\sqrt{3} + i} + \frac{i}{2} \sqrt{\sqrt{3} + i}} \right )}\right)$$
Читайте также  sqrt(2*x-3)=3
Численный ответ

x1 = 15.9697626557000

x2 = -95.8185759345000

x3 = -31.6777259237000

x4 = 31.6777259237000

x5 = 36.1283155163000

x6 = -37.9609112309000

x7 = 80.1106126665000

x8 = 25.3945406165000

x9 = 10.9955742876000

x10 = 51.8362787842000

x11 = 14.1371669412000

x12 = 56.2868683768000

x13 = -51.8362787842000

x14 = -7.85398163397000

x15 = -50.0036830696000

x16 = -23.5619449019000

x17 = 29.8451302091000

x18 = 42.4115008235000

x19 = -56.2868683768000

x20 = 64.4026493986000

x21 = -6.02138591938000

x22 = -80.1106126665000

x23 = -58.1194640914000

x24 = -100.269165527000

x25 = -91.3679863419000

x26 = 18.5877565337000

x27 = -41.1025038845000

x28 = -28.0125344945000

x29 = -19.1113553093000

x30 = 12.3045712266000

x31 = -3.40339204139000

x32 = 59.6902604182000

x33 = -67.5442420522000

x34 = -21.9911485751000

x35 = -37.6991118431000

x36 = -1.57079632679000

x37 = -15.7079632679000

x38 = 47.1238898038000

x39 = 0.0

x40 = -14.1371669412000

x41 = 86.3937979737000

x42 = -97.6511716491000

x43 = -9.68657734857000

x44 = 50.2654824574000

x45 = -63.0936524596000

x46 = -59.6902604182000

x47 = 28.2743338823000

x48 = -81.6814089933000

x49 = -12.3045712266000

x50 = 69.1150383790000

x51 = 66.2352451132000

x52 = -1385.70415962000

x53 = 72.2566310326000

x54 = 59.9520598060000

x55 = 40.5789051089000

x56 = 7.85398163397000

x57 = -65.9734457254000

x58 = -73.8274273594000

x59 = -25.3945406165000

x60 = -47.3856891916000

x61 = 34.2957198017000

x62 = -56.5486677646000

x63 = 62.5700536840000

x64 = -45.5530934771000

x65 = -69.3768377668000

x66 = -93.9859802199000

x67 = -78.2780169519000

x68 = 94.2477796077000

x69 = 20.4203522483000

x70 = -44.2440965381000

x71 = 22.2529479629000

x72 = -87.7027949127000

x73 = 53.6688744988000

x74 = -71.9948316448000

x75 = 3.14159265359000

x76 = 100.269165527000

x77 = -89.5353906273000

x78 = 78.2780169519000

x79 = 25.1327412287000

x80 = 37.9609112309000

x81 = -75.6600230740000

x82 = -53.6688744988000

x83 = 58.1194640914000

x84 = 95.8185759345000

x85 = -36.1283155163000

x86 = -29.8451302091000

x87 = 73.8274273594000

x88 = 6.28318530718000

x89 = 97.6511716491000

x90 = 63.0936524596000

x91 = 75.6600230740000

x92 = 84.5612022591000

x93 = -34.2957198017000

x94 = 81.9432083811000

x95 = 88.2263936883000

x96 = -84.5612022591000

x97 = 44.2440965381000

x98 = 9.68657734857000

x99 = 91.3679863419000

1 Звезда2 Звезды3 Звезды4 Звезды5 Звезд (Пока оценок нет)
Загрузка...