Mister Exam
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How to use it?
- Equation:
-
Equation 16x+9-4x^2=0
- Equation cos^2((2*pi/3)-x)=cos^2((2*pi/3)+x)
- Equation (x^2-16)^2+(x^2-3x-28)^2=0
-
Equation cos(2x)-cos(4x)=sin(6x)
- 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
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Identical expressions
- cos^ two ((two *pi/ three)-x)=cos^ two ((two *pi/ three)+x)
- co sinus of e of squared ((2 multiply by Pi divide by 3) minus x) equally co sinus of e of squared ((2 multiply by Pi divide by 3) plus x)
- co sinus of e of to the power of two ((two multiply by Pi divide by three) minus x) equally co sinus of e of to the power of two ((two multiply by Pi divide by three) plus x)
- cos2((2*pi/3)-x)=cos2((2*pi/3)+x)
- cos22*pi/3-x=cos22*pi/3+x
- cos²((2*pi/3)-x)=cos²((2*pi/3)+x)
- cos to the power of 2((2*pi/3)-x)=cos to the power of 2((2*pi/3)+x)
- cos^2((2pi/3)-x)=cos^2((2pi/3)+x)
- cos2((2pi/3)-x)=cos2((2pi/3)+x)
- cos22pi/3-x=cos22pi/3+x
- cos^22pi/3-x=cos^22pi/3+x
- cos^2((2*pi divide by 3)-x)=cos^2((2*pi divide by 3)+x)
-
Similar expressions
- cos^2((2*pi/3)-x)=cos^2((2*pi/3)-x)
- cos^2((2*pi/3)+x)=cos^2((2*pi/3)+x)
cos^2((2*pi/3)-x)=cos^2((2*pi/3)+x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2/2*pi \ 2/2*pi \
cos |---- - x| = cos |---- + x|
\ 3 / \ 3 /
$$\cos^{2}{\left(- x + \frac{2 \pi}{3} \right)} = \cos^{2}{\left(x + \frac{2 \pi}{3} \right)}$$
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
-pi
x2 = ----
2
$$x_{2} = - \frac{\pi}{2}$$
pi
x3 = --
2
$$x_{3} = \frac{\pi}{2}$$
x4 = pi
$$x_{4} = \pi$$
x4 = pi
Sum and product of roots
[src]
sum
pi pi - -- + -- + pi 2 2
$$\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \pi$$
=
pi
$$\pi$$
product
-pi pi 0*----*--*pi 2 2
$$\pi \frac{\pi}{2} \cdot 0 \left(- \frac{\pi}{2}\right)$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -86.3937979737193
x2 = 29.845130209103
x3 = 14.1371669411541
x4 = 48.6946861306418
x5 = -72.2566310325652
x6 = -80.1106126665397
x7 = -7.85398163397448
x8 = -59.6902604182061
x9 = -6.28318530717959
x10 = 12.5663706143592
x11 = -119.380520836412
x12 = 67.5442420521806
x13 = 56.5486677646163
x14 = -58.1194640914112
x15 = 95.8185759344887
x16 = 72.2566310325652
x17 = 37.6991118430775
x18 = 80.1106126665397
x19 = 100.530964914873
x20 = 94.2477796076938
x21 = -14.1371669411541
x22 = 7.85398163397448
x23 = -29.845130209103
x24 = 70.6858347057703
x25 = -20.4203522483337
x26 = -87.9645943005142
x27 = -31.4159265358979
x28 = 59.6902604182061
x29 = 42.4115008234622
x30 = 0.0
x31 = -17.2787595947439
x32 = -67.5442420521806
x33 = 113.097335529233
x34 = 50.2654824574367
x35 = -53.4070751110265
x36 = 45.553093477052
x37 = -45.553093477052
x38 = -21.9911485751286
x39 = -23.5619449019235
x40 = 590.619418874881
x41 = 58.1194640914112
x42 = -36.1283155162826
x43 = 87.9645943005142
x44 = -51.8362787842316
x45 = -73.8274273593601
x46 = 4.71238898038469
x47 = 64.4026493985908
x48 = -42.4115008234622
x49 = -95.8185759344887
x50 = -75.398223686155
x51 = 81.6814089933346
x52 = -65.9734457253857
x53 = -37.6991118430775
x54 = 1.5707963267949
x55 = -43.9822971502571
x56 = 20.4203522483337
x57 = 23.5619449019235
x58 = -1.5707963267949
x59 = 92.6769832808989
x60 = 6.28318530717959
x61 = 28.2743338823081
x62 = -83.2522053201295
x63 = -94.2477796076938
x64 = 86.3937979737193
x65 = 43.9822971502571
x66 = -9.42477796076938
x67 = 65.9734457253857
x68 = 31.4159265358979
x69 = 89.5353906273091
x70 = -15.707963267949
x71 = -64.4026493985908
x72 = -50.2654824574367
x73 = -48.6946861306418
x74 = 36.1283155162826
x75 = 15.707963267949
x76 = 51.8362787842316
x77 = 26.7035375555132
x78 = 73.8274273593601
x79 = -39.2699081698724
x80 = 21.9911485751286
x81 = 34.5575191894877
x82 = -97.3893722612836
x83 = -40.8407044966673
x84 = -28.2743338823081
x85 = 78.5398163397448
x86 = -89.5353906273091
x87 = -81.6814089933346
x88 = -61.261056745001
x88 = -61.261056745001