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Equation:
Equation sin(x/3)=-1/2
Equation tan(x)=-1
Equation x^4=(2*x-3)^2
Equation sin(x)=3/2
Express {x} in terms of y where:
1*x+7*y=8
4*x-13*y=13
4*x+3*y=-15
-16*x+7*y=-5
Derivative of:
sinx*cosx
Integral of d{x}:
sinx*cosx
0,25
Sum of series:
0,25
Identical expressions
sinx*cosx= zero , twenty-five
sinus of x multiply by co sinus of e of x equally 0,25
sinus of x multiply by co sinus of e of x equally zero , twenty minus five
sinxcosx=0,25
sinx*cosx=O,25
Similar expressions
2sin2x+3sinxcosx+5cos2x=0
0,2(5y-2)=0,3(2y-1)-0,9
3sinx^2-5sinxcosx-8cosx^2=0

sinx*cosx=0,25 equation

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

The solution

You have entered [src]

sin(x)*cos(x) = 1/4

$$\sin{\left(x \right)} \cos{\left(x \right)} = \frac{1}{4}$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

           /                  ___________\
           |       ___       /       ___ |
x1 = 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /

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

            /                 ___________\
            |      ___       /       ___ |
x2 = -2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /

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

            /                 ___________\
            |      ___       /       ___ |
x3 = -2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /

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

            /                 ___________\
            |      ___       /       ___ |
x4 = -2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /

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

x4 = -2*atan(-2*sqrt(sqrt(3) + 2) + sqrt(3) + 2)

Sum and product of roots [src]

sum

      /                  ___________\         /                 ___________\         /                 ___________\         /                 ___________\
      |       ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |
2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  / - 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  / - 2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  / - 2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /

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

        /                 ___________\         /                 ___________\         /                 ___________\         /                  ___________\
        |      ___       /       ___ |         |      ___       /       ___ |         |      ___       /       ___ |         |       ___       /       ___ |
- 2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  / - 2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  / - 2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  / + 2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /

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

product

      /                  ___________\        /                 ___________\        /                 ___________\        /                 ___________\
      |       ___       /       ___ |        |      ___       /       ___ |        |      ___       /       ___ |        |      ___       /       ___ |
2*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*-2*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /*-2*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /*-2*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /

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

        /                  ___________\     /                 ___________\     /                 ___________\     /                 ___________\
        |       ___       /       ___ |     |      ___       /       ___ |     |      ___       /       ___ |     |      ___       /       ___ |
-16*atan\-2 + \/ 3  + 2*\/  2 - \/ 3  /*atan\2 + \/ 3  - 2*\/  2 + \/ 3  /*atan\2 + \/ 3  + 2*\/  2 + \/ 3  /*atan\2 - \/ 3  + 2*\/  2 - \/ 3  /

$$- 16 \operatorname{atan}{\left(-2 + 2 \sqrt{2 - \sqrt{3}} + \sqrt{3} \right)} \operatorname{atan}{\left(- \sqrt{3} + 2 \sqrt{2 - \sqrt{3}} + 2 \right)} \operatorname{atan}{\left(\sqrt{3} + 2 + 2 \sqrt{\sqrt{3} + 2} \right)} \operatorname{atan}{\left(- 2 \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2 \right)}$$

-16*atan(-2 + sqrt(3) + 2*sqrt(2 - sqrt(3)))*atan(2 + sqrt(3) - 2*sqrt(2 + sqrt(3)))*atan(2 + sqrt(3) + 2*sqrt(2 + sqrt(3)))*atan(2 - sqrt(3) + 2*sqrt(2 - sqrt(3)))

Numerical answer [src]

x1 = -75.1364242983559

x2 = 29.5833308213039

x3 = -1.83259571459405

x4 = 0.261799387799149

x5 = 73.565627971561

x6 = 12.8281700021583

x7 = 51.5744793964324

x8 = 15.9697626557481

x9 = -74.0892267471593

x10 = 13.8753675533549

x11 = -52.0980781720307

x12 = 72.5184304203644

x13 = -100.269165527074

x14 = 45.2912940892529

x15 = -67.8060414399797

x16 = 81.9432083811338

x17 = -53.1452757232273

x18 = 6.54498469497874

x19 = 34.8193185772869

x20 = 44.2440965380563

x21 = 4.45058959258554

x22 = -83.5140047079287

x23 = 50.5272818452358

x24 = -81.4196096055355

x25 = 9.68657734856853

x26 = 88.2263936883134

x27 = -17.540558982543

x28 = 26.4417381677141

x29 = -80.3724120543389

x30 = -59.4284610304069

x31 = 42.1497014356631

x32 = 28.5361332701073

x33 = 94.5095789954929

x34 = -9.16297857297023

x35 = -42.6733002112614

x36 = 79.8488132787406

x37 = -65.7116463375865

x38 = -36.3901149040818

x39 = 59.9520598060052

x40 = 20.1585528605345

x41 = 78.801615727544

x42 = 7.59218224617533

x43 = -86.6555973615185

x44 = -28.012534494509

x45 = -23.8237442897226

x46 = -8.11578102177363

x47 = 95.5567765466895

x48 = -55.2396708256205

x49 = 31.6777259236971

x50 = 53.6688744988256

x51 = 100.792764302673

x52 = -58.3812634792103

x53 = -40.5789051088682

x54 = -56.2868683768171

x55 = 35.8665161284835

x56 = -34.2957198016886

x57 = 56.8104671524154

x58 = -30.1069295969022

x59 = -21.7293491873294

x60 = -14.3989663289532

x61 = -12.30457122656

x62 = -89.7971900151083

x63 = -87.7027949127151

x64 = -71.9948316447661

x65 = 57.857664703612

x66 = 75.6600230739542

x67 = -15.4461638801498

x68 = -31.1541271480988

x69 = -61.5228561328001

x70 = -39.5317075576716

x71 = 37.9609112308767

x72 = -43.720497762458

x73 = -45.8148928648512

x74 = 48.4328867428426

x75 = -96.0803753222878

x76 = -6.02138591938044

x77 = -64.6644487863899

x78 = -694.030177055545

x79 = 66.2352451131848

x80 = -37.4373124552784

x81 = 86.1319985859202

x82 = -50.0036830696375

x83 = 64.1408500107916

x84 = -97.1275728734844

x85 = -78.2780169519457

x86 = 22.2529479629277

x87 = 70.4240353179712

x88 = 92.4151838930998

x89 = -93.9859802198946

x89 = -93.9859802198946

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Identical expressions

Similar expressions

sinx*cosx=0,25 equation

Numerical solution:

The solution