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Equation:
Equation 6sin^2x+sin2x=2
Equation cos(pi(x+1))/2=-1
Equation cos(x+pi/3)=0
Equation sin(3*x-pi/4)=sqrt(3)/2
Express {x} in terms of y where:
15*x+15*y=16
-4*x+18*y=-14
8*x+7*y=-13
-12*x+3*y=-9
Identical expressions
6sin^ two x+sin2x=2
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6sin²x+sin2x=2
6sin to the power of 2x+sin2x=2
Similar expressions
6sin^2x-sin2x=2

6sin^2x+sin2x=2 equation

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

The solution

You have entered [src]

     2                  
6*sin (x) + sin(2*x) = 2

$$6 \sin^{2}{\left(x \right)} + \sin{\left(2 x \right)} = 2$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

  pi           /log(5)      /  ___\\                 /log(5)      /  ___\\                    /    5/2\
- -- + -pi + I*|------ - log\\/ 5 /| + atan(1/2) + I*|------ - log\\/ 5 /| + atan(1/2) - I*log\(-I)   /
  4            \  2                /                 \  2                /

$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + \left(\left(- \frac{\pi}{4} + \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)\right)$$

              5*pi        /    5/2\       /log(5)      /  ___\\
2*atan(1/2) - ---- - I*log\(-I)   / + 2*I*|------ - log\\/ 5 /|
               4                          \  2                /

$$- \frac{5 \pi}{4} + 2 \operatorname{atan}{\left(\frac{1}{2} \right)} - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} + 2 i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)$$

product

-pi  /        /log(5)      /  ___\\            \ /  /log(5)      /  ___\\            \ /      /    5/2\\
----*|-pi + I*|------ - log\\/ 5 /| + atan(1/2)|*|I*|------ - log\\/ 5 /| + atan(1/2)|*\-I*log\(-I)   //
 4   \        \  2                /            / \  \  2                /            /

$$- i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} - \frac{\pi}{4} \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(\frac{1}{2} \right)} + i \left(- \log{\left(\sqrt{5} \right)} + \frac{\log{\left(5 \right)}}{2}\right)\right)$$

                                    /    5/2\
pi*I*(-pi + atan(1/2))*atan(1/2)*log\(-I)   /
---------------------------------------------
                      4

$$\frac{i \pi \left(- \pi + \operatorname{atan}{\left(\frac{1}{2} \right)}\right) \log{\left(\left(- i\right)^{\frac{5}{2}} \right)} \operatorname{atan}{\left(\frac{1}{2} \right)}}{4}$$

pi*i*(-pi + atan(1/2))*atan(1/2)*log((-i)^(5/2))/4

Rapid solution [src]

     -pi 
x1 = ----
      4

$$x_{1} = - \frac{\pi}{4}$$

             /log(5)      /  ___\\            
x2 = -pi + I*|------ - log\\/ 5 /| + atan(1/2)
             \  2                /

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

       /log(5)      /  ___\\            
x3 = I*|------ - log\\/ 5 /| + atan(1/2)
       \  2                /

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

           /    5/2\
x4 = -I*log\(-I)   /

$$x_{4} = - i \log{\left(\left(- i\right)^{\frac{5}{2}} \right)}$$

x4 = -i*log((-i)^(5/2))

Numerical answer [src]

x1 = 47.5875374128477

x2 = -66.7588438887831

x3 = -49.8018348484359

x4 = 55.7632696012188

x5 = -47.9092879672443

x6 = 46.3384916404494

x7 = -76.1836218495525

x8 = 90.3207887907066

x9 = -21.5275009661277

x10 = -87.5009466915134

x11 = -98.174770424681

x12 = -10.2101761241668

x13 = -93.784131998693

x14 = -85.6083998103219

x15 = -126.449104306989

x16 = 18.0641577581413

x17 = 9.88842556977019

x18 = 0.463647609000806

x19 = 97.8530198702844

x20 = -91.8915851175014

x21 = -5.81953769817878

x22 = 77.7544181763474

x23 = -13.3517687777566

x24 = -3.92699081698724

x25 = -78.076168730744

x26 = 88.428241909515

x27 = 3.6052402625906

x28 = -40.3770568876665

x29 = 40.0553063332699

x30 = -25.9181393921158

x31 = 33.7721210260903

x32 = -43.5186495412563

x33 = 16.1716108769498

x34 = 44.4459447592579

x35 = 2.35619449019234

x36 = 99.7455667514759

x37 = -27.8106862733073

x38 = 96.6039740978861

x39 = 38.1627594520783

x40 = 25.5963888377192

x41 = -12.1027230053584

x42 = 84.037603483527

x43 = -84.3593540379236

x44 = -56.0850201556155

x45 = 24.3473430653209

x46 = 66.4370933343865

x47 = 75.8618712951559

x48 = -62.3682054627951

x49 = -65.5097981163849

x50 = -71.7929834235644

x51 = -18.385908312538

x52 = 69.5786859879763

x53 = 1486.43697275697

x54 = 62.0464549083984

x55 = -57.3340659280137

x56 = 60.1539080272069

x57 = 8.63937979737193

x58 = 159.435827169682

x59 = -69.9004365423729

x60 = 68.329640215578

x61 = -63.6172512351933

x62 = 31.8795741448987

x63 = -19.6349540849362

x64 = 91.5698345631048

x65 = -41.6261026600648

x66 = -100.067317305873

x67 = 53.8707227200273

x68 = 30.6305283725005

x69 = -34.0938715804869

x70 = 74.6128255227576

x71 = -79.3252145031423

x72 = 52.621676947629

x73 = 11.7809724509617

x74 = 22.4547961841294

x75 = -54.1924732744239

x76 = -32.2013246992954

x77 = -35.3429173528852

x78 = 82.1450566023354

x78 = 82.1450566023354

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Similar expressions

6sin^2x+sin2x=2 equation

Numerical solution:

The solution