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Equation:
Equation 4x+2(1-3x)=13
Equation x^2-10x+25=0
Equation x-y=0
Equation 3-x=1+x
Express {x} in terms of y where:
-2*x-4*y=11
14*x-3*y=-9
6*x-19*y=-18
10*x-5*y=3
Identical expressions
sin2x+16cos^2x= four
sinus of 2x plus 16 co sinus of e of squared x equally 4
sinus of 2x plus 16 co sinus of e of squared x equally four
sin2x+16cos2x=4
sin2x+16cos²x=4
sin2x+16cos to the power of 2x=4
Similar expressions
sin2x-16cos^2x=4

sin2x+16cos^2x=4 equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

                 2       
sin(2*x) + 16*cos (x) = 4

$$\sin{\left(2 x \right)} + 16 \cos^{2}{\left(x \right)} = 4$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

             /log(5)      /  ___\\          
x1 = -pi + I*|------ - log\\/ 5 /| + atan(2)
             \  2                /

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

       /log(5)      /  ___\\          
x2 = I*|------ - log\\/ 5 /| + atan(2)
       \  2                /

$$x_{2} = \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$

                        /log(13)      /  ____\\
x3 = pi - atan(3/2) + I*|------- - log\\/ 13 /|
                        \   2                 /

$$x_{3} = - \operatorname{atan}{\left(\frac{3}{2} \right)} + \pi + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$

                    /log(13)      /  ____\\
x4 = -atan(3/2) + I*|------- - log\\/ 13 /|
                    \   2                 /

$$x_{4} = - \operatorname{atan}{\left(\frac{3}{2} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$

x4 = -atan(3/2) + i*(-log(sqrt(13)) + log(13)/2)

Sum and product of roots [src]

sum

        /log(5)      /  ___\\               /log(5)      /  ___\\                                /log(13)      /  ____\\                  /log(13)      /  ____\\
-pi + I*|------ - log\\/ 5 /| + atan(2) + I*|------ - log\\/ 5 /| + atan(2) + pi - atan(3/2) + I*|------- - log\\/ 13 /| + -atan(3/2) + I*|------- - log\\/ 13 /|
        \  2                /               \  2                /                                \   2                 /                  \   2                 /

$$\left(\left(\left(- \pi + \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) + \left(\operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{3}{2} \right)} + \pi + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{3}{2} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right)$$

                               /log(5)      /  ___\\       /log(13)      /  ____\\
-2*atan(3/2) + 2*atan(2) + 2*I*|------ - log\\/ 5 /| + 2*I*|------- - log\\/ 13 /|
                               \  2                /       \   2                 /

$$- 2 \operatorname{atan}{\left(\frac{3}{2} \right)} + 2 \operatorname{atan}{\left(2 \right)} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right) + 2 i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)$$

product

/        /log(5)      /  ___\\          \ /  /log(5)      /  ___\\          \ /                   /log(13)      /  ____\\\ /               /log(13)      /  ____\\\
|-pi + I*|------ - log\\/ 5 /| + atan(2)|*|I*|------ - log\\/ 5 /| + atan(2)|*|pi - atan(3/2) + I*|------- - log\\/ 13 /||*|-atan(3/2) + I*|------- - log\\/ 13 /||
\        \  2                /          / \  \  2                /          / \                   \   2                 // \               \   2                 //

$$\left(\operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \pi + \operatorname{atan}{\left(2 \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(- \operatorname{atan}{\left(\frac{3}{2} \right)} + \pi + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right) \left(- \operatorname{atan}{\left(\frac{3}{2} \right)} + i \left(- \log{\left(\sqrt{13} \right)} + \frac{\log{\left(13 \right)}}{2}\right)\right)$$

/  2                                                \                  
\pi  + atan(2)*atan(3/2) - pi*atan(2) - pi*atan(3/2)/*atan(2)*atan(3/2)

$$\left(- \pi \operatorname{atan}{\left(2 \right)} - \pi \operatorname{atan}{\left(\frac{3}{2} \right)} + \operatorname{atan}{\left(\frac{3}{2} \right)} \operatorname{atan}{\left(2 \right)} + \pi^{2}\right) \operatorname{atan}{\left(\frac{3}{2} \right)} \operatorname{atan}{\left(2 \right)}$$

(pi^2 + atan(2)*atan(3/2) - pi*atan(2) - pi*atan(3/2))*atan(2)*atan(3/2)

Numerical answer [src]

x1 = 39.85791077342

x2 = 54.5142238288206

x3 = -2.0344439357957

x4 = -74.2910749683609

x5 = 33.5747254662404

x6 = -68.0078896611814

x7 = 24.149947505471

x8 = 46.1410960805996

x9 = 63.93900178959

x10 = -33.4503704716936

x11 = 60.7974091360002

x12 = 68.1322446557281

x13 = -54.3898688342738

x14 = 32.523075253692

x15 = 38.8062605608716

x16 = 76.5053724039491

x17 = 99.5481711916261

x18 = 74.4154299629077

x19 = -82.664202716582

x20 = 8.44198423752205

x21 = -32.3987202591453

x22 = 52.4242813877792

x23 = 27.2915401590608

x24 = 11.5835768911118

x25 = -48.1066835270942

x26 = 85.9301503647185

x27 = -77.4326676219507

x28 = 26.2398899465124

x29 = 70.2221870967695

x30 = 90.1233932308567

x31 = 48.231038521641

x32 = -63.8146467950432

x33 = -13.5491643376065

x34 = -76.3810174094024

x35 = -93.1406308898997

x36 = -41.8234982199146

x37 = -49.1583337396426

x38 = -39.7335557788732

x39 = 4.24874137138388

x40 = -8.31762924297529

x41 = -30.3087778181038

x42 = -4.12438637683712

x43 = 17.8667621982914

x44 = -79.5226100629922

x45 = 2.15879893034246

x46 = 35.6646679072818

x47 = -89.9990382363099

x48 = 30.4331328126506

x49 = -98.3721659845309

x50 = -17.7424072037447

x51 = -96.2822235434895

x52 = 57.6558164824104

x53 = 41.9478532144614

x54 = -85.8057953701718

x55 = -60.6730541414534

x56 = -55.4415190468222

x57 = 96.4065785380363

x58 = 13.6735193321533

x59 = 61.8490593485485

x60 = -36.5919631252834

x61 = 55.565874041369

x62 = -10.4075716840167

x63 = 101.638113632667

x64 = -61.7247043540018

x65 = -26.1155349519657

x66 = -19.8323496447861

x67 = -46.0167410860528

x68 = -35.5403129127351

x69 = -27.167185164514

x70 = 83.8402079236771

x71 = -11.4592218965651

x72 = -24.0255925109243

x73 = 16.8151119857431

x74 = -57.5314614878636

x75 = -92.0889806773513

x76 = 77.5570226164975

x77 = 19.9567046393328

x78 = 92.2133356718981

x79 = -5.1760365893855

x80 = 10.5319266785635

x81 = 98.4965209790777

x82 = -71.1494823147711

x83 = -70.0978321022228

x84 = -99.4238161970793

x85 = -52.2999263932324

x86 = 82.7885577111287

x87 = -83.7158529291303

x87 = -83.7158529291303

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Identical expressions

Similar expressions

sin2x+16cos^2x=4 equation

Numerical solution:

The solution