Mister Exam

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Equation:
Equation sqrt(4×cos^2+6)+sqrt(4×sin^2+8)=6
Equation (4cos2x-9sinx-4)lg(-cosx)=0
Equation x^4+5x^2-36=0
Equation 2sinx=5cosx
Express {x} in terms of y where:
5*x-5*y=20
8*x-7*y=-13
15*x-15*y=16
9*x+18*y=6
Identical expressions
sqrt(four ×cos^ two + six)+sqrt(four ×sin^ two + eight)= six
square root of (4× co sinus of e of squared plus 6) plus square root of (4× sinus of squared plus 8) equally 6
square root of (four × co sinus of e of to the power of two plus six) plus square root of (four × sinus of to the power of two plus eight) equally six
√(4×cos^2+6)+√(4×sin^2+8)=6
sqrt(4×cos2+6)+sqrt(4×sin2+8)=6
sqrt4×cos2+6+sqrt4×sin2+8=6
sqrt(4×cos²+6)+sqrt(4×sin²+8)=6
sqrt(4×cos to the power of 2+6)+sqrt(4×sin to the power of 2+8)=6
sqrt4×cos^2+6+sqrt4×sin^2+8=6
Similar expressions
sqrt(4×cos^2+6)+sqrt(4×sin^2-8)=6
sqrt(4×cos^2-6)+sqrt(4×sin^2+8)=6
sqrt(4×cos^2+6)-sqrt(4×sin^2+8)=6

sqrt(4×cos^2+6)+sqrt(4×sin^2+8)=6 equation

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

You have entered [src]

   _______________      _______________    
  /      2             /      2            
\/  4*cos (x) + 6  + \/  4*sin (x) + 8  = 6

$$\sqrt{4 \sin^{2}{\left(x \right)} + 8} + \sqrt{4 \cos^{2}{\left(x \right)} + 6} = 6$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     -5*pi
x1 = -----
       6

$$x_{1} = - \frac{5 \pi}{6}$$

     -pi 
x2 = ----
      6

$$x_{2} = - \frac{\pi}{6}$$

     pi
x3 = --
     6

$$x_{3} = \frac{\pi}{6}$$

     5*pi
x4 = ----
      6

$$x_{4} = \frac{5 \pi}{6}$$

x4 = 5*pi/6

Sum and product of roots [src]

sum

  5*pi   pi   pi   5*pi
- ---- - -- + -- + ----
   6     6    6     6

$$\left(\left(- \frac{5 \pi}{6} - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{5 \pi}{6}$$

$$0$$

product

-5*pi -pi  pi 5*pi
-----*----*--*----
  6    6   6   6

$$\frac{5 \pi}{6} \frac{\pi}{6} \cdot - \frac{5 \pi}{6} \left(- \frac{\pi}{6}\right)$$

     4
25*pi 
------
 1296

$$\frac{25 \pi^{4}}{1296}$$

25*pi^4/1296

Numerical answer [src]

x1 = 75.9218225372795

x2 = 9.94837678913051

x3 = -49.7418836876391

x4 = -60.2138591513176

x5 = -44.5058962845439

x6 = -16.2315620167585

x7 = 44.5058959435447

x8 = 78.0162175404366

x9 = 49.7418836577074

x10 = -79.0634152004172

x11 = -90.5825879396456

x12 = 41.364303459495

x13 = -31.93952555286

x14 = 27.7507351052594

x15 = -21.4675496421681

x16 = -486.42326445147

x17 = -0.52359891673777

x18 = 60.2138592265084

x19 = 97.9129711196

x20 = 16.2315620585981

x21 = 69.6386373992622

x22 = -2.61799366908793

x23 = 0.523598866401086

x24 = 18.3259570920346

x25 = 5.75958654641785

x26 = 84.2994028358295

x27 = -16.2315624303204

x28 = -599.520596578632

x29 = 53.930673954777

x30 = -84.2994026526006

x31 = -25.6563400703144

x32 = 47.6474888209138

x33 = -68.5914393706255

x34 = -40.3171054941467

x35 = 25.6563402423929

x36 = -38.2227105829563

x37 = 85.3466005820031

x38 = -71.7330322686127

x39 = -9.94837688852468

x40 = 22.5147473980188

x41 = 93.7241807280412

x42 = 12.042771738946

x43 = -46.6002908024587

x44 = -69.6386372325306

x45 = -85.3466006609947

x46 = -69.6386365667511

x47 = -97.9129706317612

x48 = 90.5825879688458

x49 = -3.66519148915675

x50 = 24.6091422314933

x51 = -19.3731549260064

x52 = 52.8834761459692

x53 = -41.3643035045126

x54 = -100.007366130678

x55 = -63.3554520828451

x56 = -91.6297858135889

x57 = 82.2050078120736

x58 = -53.9306740183258

x59 = 56.0250689473018

x60 = 3.66519166370547

x61 = 85.3465988881817

x62 = -79.0634156702199

x63 = -35.0811180939198

x64 = 66.4970444978452

x65 = -5.75958652411242

x66 = -62.3082540733009

x67 = 71.7330322004504

x68 = -57.0722665316892

x69 = -47.647488651439

x70 = 68.5914393895909

x71 = -34.0339203775964

x72 = 63.355452021603

x73 = -13.0899695369491

x74 = -93.7241808491355

x75 = 74.8746247102483

x76 = 40.3171056732612

x77 = -18.3259569151429

x78 = -27.7507351061619

x79 = 38.2227106420866

x80 = 96.8657732758874

x81 = -43.4586981120301

x82 = -57.0722666484932

x83 = 88.488193057936

x84 = -78.0162175458139

x85 = -82.2050077212707

x86 = 34.0339203481318

x87 = 8.90117902217255

x88 = -24.6091422352421

x89 = -79.0634153539698

x90 = 19.3731548958743

x91 = 46.6002908104711

x92 = 91.6297859774318

x93 = 62.3082542545251

x94 = -65.449846540761

x95 = 30.892327583215

x96 = 31.93952537207

x97 = 313.635667030822

x98 = -12.0427717940768

x99 = 100.007366129651

x100 = 2.61799365266497

x101 = -56.0250689614846

x101 = -56.0250689614846