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  • Equation:
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  • Equation cos(x)=sqrt(2)/2 Equation cos(x)=sqrt(2)/2
  • Equation (7x+9)-(11x-7)=8 Equation (7x+9)-(11x-7)=8
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  • Express {x} in terms of y where:
  • -1*x+19*y=-10
  • 10*x+9*y=-4
  • 9*x-18*y=6
  • -10*x-16*y=-6

  • Identical expressions

  • (nine ^(sin(two x))- three ^(two *sqrt(2)*sinx))/(sqrt(eleven *sinx))= zero
  • (9 to the power of ( sinus of (2x)) minus 3 to the power of (2 multiply by square root of (2) multiply by sinus of x)) divide by ( square root of (11 multiply by sinus of x)) equally 0
  • (nine to the power of ( sinus of (two x)) minus three to the power of (two multiply by square root of (2) multiply by sinus of x)) divide by ( square root of (eleven multiply by sinus of x)) equally zero
  • (9^(sin(2x))-3^(2*√(2)*sinx))/(√(11*sinx))=0
  • (9(sin(2x))-3(2*sqrt(2)*sinx))/(sqrt(11*sinx))=0
  • 9sin2x-32*sqrt2*sinx/sqrt11*sinx=0
  • (9^(sin(2x))-3^(2sqrt(2)sinx))/(sqrt(11sinx))=0
  • (9(sin(2x))-3(2sqrt(2)sinx))/(sqrt(11sinx))=0
  • 9sin2x-32sqrt2sinx/sqrt11sinx=0
  • 9^sin2x-3^2sqrt2sinx/sqrt11sinx=0
  • (9^(sin(2x))-3^(2*sqrt(2)*sinx))/(sqrt(11*sinx))=O
  • (9^(sin(2x))-3^(2*sqrt(2)*sinx)) divide by (sqrt(11*sinx))=0

  • Similar expressions

  • (9^(sin(2x))+3^(2*sqrt(2)*sinx))/(sqrt(11*sinx))=0

(9^(sin(2x))-3^(2*sqrt(2)*sinx))/(sqrt(11*sinx))=0 equation

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Numerical solution:

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The solution

You have entered [src] 
                 ___           
 sin(2*x)    2*\/ 2 *sin(x)    
9         - 3                  
--------------------------- = 0
         ___________           
       \/ 11*sin(x)
$$\frac{- 3^{2 \sqrt{2} \sin{\left(x \right)}} + 9^{\sin{\left(2 x \right)}}}{\sqrt{11 \sin{\left(x \right)}}} = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     -pi 
x1 = ----
      4
$$x_{1} = - \frac{\pi}{4}$$ 
     pi
x2 = --
     4
$$x_{2} = \frac{\pi}{4}$$ 
x2 = pi/4
Sum and product of roots [src] 
sum
  pi   pi
- -- + --
  4    4
$$- \frac{\pi}{4} + \frac{\pi}{4}$$ 
=
0
$$0$$ 
product
-pi  pi
----*--
 4   4
$$- \frac{\pi}{4} \frac{\pi}{4}$$ 
=
   2 
-pi  
-----
  16
$$- \frac{\pi^{2}}{16}$$ 
-pi^2/16
Numerical answer [src] 
x1 = 25.9181393921158
x2 = 87.1791961371168
x3 = 63.6172512351933
x4 = 49.4800842940392
x5 = -95.0331777710912
x6 = -47.1238898038469 + 0.680393433142602*i
x7 = -44.7676953136546
x8 = -78.5398163397448 + 1.55155746322036*i
x9 = 11.7809724509617
x10 = 9.42477796076938 + 0.680393433142602*i
x11 = -25.9181393921158
x12 = -57.3340659280137
x13 = 93.4623814442964
x14 = -36.9137136796801
x15 = -7.06858347057703
x16 = -99.7455667514759
x17 = 74.6128255227576
x18 = 68.329640215578
x19 = -24.3473430653209
x20 = -20.2638318602414 - 16.8706944088928*i
x21 = 36.9137136796801
x22 = 43.1968989868597
x23 = -19.6349540849362
x24 = 18.0641577581413
x25 = -88.7499924639117
x26 = -34.5575191894877 + 0.680393433142602*i
x27 = -3.14159265358979 + 0.680393433142602*i
x28 = 84.8230016469244 + 0.680393433142602*i
x29 = 32.2013246992954
x30 = -76.1836218495525
x31 = 80.8960108299372
x32 = 40.8407044966673 + 0.680393433142602*i
x33 = -69.9004365423729
x34 = -51.0508806208341
x35 = -13.3517687777566
x36 = -55.7632696012188
x37 = -0.785398163397448
x38 = -32.2013246992954
x39 = 24.3473430653209
x40 = -38.484510006475
x41 = -65.9734457253857 + 0.680393433142602*i
x42 = 76.1836218495525
x43 = 7.06858347057703
x44 = 30.6305283725005
x45 = -68.329640215578
x46 = 11.1756107638158 - 1.4262072366726*i
x47 = 69.9004365423729
x48 = 55.7632696012188
x49 = 62.0464549083984
x50 = 99.7455667514759
x51 = 5.49778714378214
x52 = 19.6349540849362
x53 = -11.7809724509617
x54 = -18.0641577581413
x55 = -82.4668071567321
x56 = -62.0464549083984
x57 = -63.6172512351933
x57 = -63.6172512351933
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