1+4*sin(x)*cos(y)=0 1+4*sin(y)*cos(x)=0

Дано

$$4 \sin{\left (x \right )} \cos{\left (y \right )} + 1 = 0$$

1 + 4*sin(y)*cos(x) = 0

$$4 \sin{\left (y \right )} \cos{\left (x \right )} + 1 = 0$$
Ответ
$$x_{1} = {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )} \right )}} \right )} + \pi$$
=
$${asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )} \right )}} \right )} + \pi$$
=

4.45058959258554

$$y_{1} = 2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )}$$
=
$$2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )}$$
=

1.30899693899575

$$x_{2} = {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )} \right )}} \right )} + \pi$$
=
$${asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )} \right )}} \right )} + \pi$$
=

1.83259571459405

$$y_{2} = 2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )}$$
=
$$2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )}$$
=

1.83259571459405

$$x_{3} = {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )} \right )}} \right )} + \pi$$
=
$${asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )} \right )}} \right )} + \pi$$
=

2.87979326579064

$$y_{3} = 2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )}$$
=
$$2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )}$$
=

2.87979326579064

$$x_{4} = {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )} \right )}} \right )} + \pi$$
=
$${asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )} \right )}} \right )} + \pi$$
=

3.40339204138894

$$y_{4} = — 2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )}$$
=
$$- 2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )}$$
=

0.261799387799149

$$x_{5} = — {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )} \right )}} \right )}$$
=
$$- {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )} \right )}} \right )}$$
=

-1.30899693899575

$$y_{5} = — 2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )}$$
=
$$- 2 {atan}{\left (-2 + 2 \sqrt{- \sqrt{3} + 2} + \sqrt{3} \right )}$$
=

-1.30899693899575

$$x_{6} = — {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )} \right )}} \right )}$$
=
$$- {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )} \right )}} \right )}$$
=

1.30899693899575

$$y_{6} = — 2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )}$$
=
$$- 2 {atan}{\left (- \sqrt{3} + 2 \sqrt{- \sqrt{3} + 2} + 2 \right )}$$
=

-1.83259571459405

$$x_{7} = — {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )} \right )}} \right )}$$
=
$$- {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )} \right )}} \right )}$$
=

0.261799387799149

$$y_{7} = — 2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )}$$
=
$$- 2 {atan}{\left (\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right )}$$
=

-2.87979326579064

$$x_{8} = — {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )} \right )}} \right )}$$
=
$$- {asin}{\left (\frac{1}{4 \cos{\left (2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )} \right )}} \right )}$$
=

-0.261799387799149

$$y_{8} = 2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )}$$
=
$$2 {atan}{\left (- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right )}$$
=

-0.261799387799149

Численный ответ
Читайте также  617*x/250+47*y/1000+15/4=0 47*x/1000+47*y/500-11/4=0

x1 = -1.308996938995747
y1 = -1.308996938995747

x2 = -6.021385919380437
y2 = -2.879793265790644

x3 = 6.021385919380437
y3 = 6.021385919380437

x4 = -1.832595714594046
y4 = 1.308996938995747

x5 = 6.544984694978736
y5 = 9.686577348568529

x6 = -6.544984694978736
y6 = 6.021385919380437

x7 = -14.39896632895322
y7 = 1.308996938995747

x8 = -6.021385919380437
y8 = 9.686577348568529

x9 = -1.832595714594046
y9 = 13.87536755335492

x10 = -9.16297857297023
y10 = -6.021385919380437

x11 = -6.544984694978736
y11 = -6.544984694978736

x12 = 1.832595714594046
y12 = 1.832595714594046

x13 = 8.115781021773633
y13 = 8.115781021773633

x14 = -10.73377489976513
y14 = 1.832595714594046

x15 = -9.686577348568529
y15 = -9.686577348568529

x16 = -9.16297857297023
y16 = 6.544984694978736

x17 = 2.879793265790644
y17 = 15.44616388014982

x18 = 7.592182246175334
y18 = 10.73377489976513

x19 = -9.686577348568529
y19 = 9.16297857297023

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