Mister Exam
x*siny=0.66; x*cosy=0.975
The solution
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[src]
33
x*sin(y) = --
50
$$x \sin{\left(y \right)} = \frac{33}{50}$$
39
x*cos(y) = --
40
$$x \cos{\left(y \right)} = \frac{39}{40}$$
x*cos(y) = 39/40
Rapid solution
$$x_{1} = - \frac{3 \sqrt{6161}}{200}$$
=
$$- \frac{3 \sqrt{6161}}{200}$$
=
$$y_{1} = - 2 \operatorname{atan}{\left(\frac{65}{44} + \frac{\sqrt{6161}}{44} \right)}$$
=
$$- 2 \operatorname{atan}{\left(\frac{65}{44} + \frac{\sqrt{6161}}{44} \right)}$$
=
=
$$- \frac{3 \sqrt{6161}}{200}$$
=
-1.17738056719142
$$y_{1} = - 2 \operatorname{atan}{\left(\frac{65}{44} + \frac{\sqrt{6161}}{44} \right)}$$
=
$$- 2 \operatorname{atan}{\left(\frac{65}{44} + \frac{\sqrt{6161}}{44} \right)}$$
=
-2.54652302988425
$$x_{2} = \frac{3 \sqrt{6161}}{200}$$
=
$$\frac{3 \sqrt{6161}}{200}$$
=
$$y_{2} = - 2 \operatorname{atan}{\left(\frac{65}{44} - \frac{\sqrt{6161}}{44} \right)}$$
=
$$- 2 \operatorname{atan}{\left(\frac{65}{44} - \frac{\sqrt{6161}}{44} \right)}$$
=
=
$$\frac{3 \sqrt{6161}}{200}$$
=
1.17738056719142
$$y_{2} = - 2 \operatorname{atan}{\left(\frac{65}{44} - \frac{\sqrt{6161}}{44} \right)}$$
=
$$- 2 \operatorname{atan}{\left(\frac{65}{44} - \frac{\sqrt{6161}}{44} \right)}$$
=
0.595069623705541
Numerical answer
[src]
x1 = -1.177380567191424 y1 = 3.736662277295334
x2 = -1.177380567191424 y2 = -8.829708337063839
x3 = -1.177380567191424 y3 = -2.546523029884252
x4 = 1.177380567191424 y4 = -5.688115683474045
x5 = 1.177380567191424 y5 = 6.878254930885128
x6 = -1.177380567191424 y6 = 10.01984758447492
x7 = 1.177380567191424 y7 = 0.5950696237055412
x7 = 1.177380567191424 y7 = 0.5950696237055412