Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2+3x=-2x-13
-
Equation cos(x)=-(1/2)
-
Equation x^3+4*x^2-x-4=0
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Equation 2x-5=7
- Express {x} in terms of y where:
- -11*x+6*y=4
- 14*x-13*y=-10
- -1*x-7*y=5
- 10*x+1*y=10
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Identical expressions
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)= zero
- ( square root of 2 multiply by sinus of squared x plus co sinus of e of x minus square root of 2) multiply by ( square root of 6 multiply by sinus of x) equally 0
- ( square root of 2 multiply by sinus of squared x plus co sinus of e of x minus square root of 2) multiply by ( square root of 6 multiply by sinus of x) equally zero
- (√2*sin^2x+cosx-√2)*(√6*sinx)=0
- (sqrt2*sin2x+cosx-sqrt2)*(sqrt6*sinx)=0
- sqrt2*sin2x+cosx-sqrt2*sqrt6*sinx=0
- (sqrt2*sin²x+cosx-sqrt2)*(sqrt6*sinx)=0
- (sqrt2*sin to the power of 2x+cosx-sqrt2)*(sqrt6*sinx)=0
- (sqrt2sin^2x+cosx-sqrt2)(sqrt6sinx)=0
- (sqrt2sin2x+cosx-sqrt2)(sqrt6sinx)=0
- sqrt2sin2x+cosx-sqrt2sqrt6sinx=0
- sqrt2sin^2x+cosx-sqrt2sqrt6sinx=0
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=O
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Similar expressions
- (sqrt2*sin^2x+cosx+sqrt2)*(sqrt6*sinx)=0
- (sqrt2*sin^2x-cosx-sqrt2)*(sqrt6*sinx)=0
(sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ ___ 2 ___\ ___ \\/ 2 *sin (x) + cos(x) - \/ 2 /*\/ 6 *sin(x) = 0
$$\sqrt{6} \sin{\left(x \right)} \left(\left(\sqrt{2} \sin^{2}{\left(x \right)} + \cos{\left(x \right)}\right) - \sqrt{2}\right) = 0$$
Sum and product of roots
[src]
sum
/ ____________\ / ____________\
| / ___ | | / ___ |
pi pi |\/ -1 + \/ 2 | |\/ -1 + \/ 2 |
- -- + -- - 2*atan|---------------| + 2*atan|---------------|
2 2 | ___________| | ___________|
| / ___ | | / ___ |
\ \/ 1 + \/ 2 / \ \/ 1 + \/ 2 /
$$\left(- 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)} + \left(- \frac{\pi}{2} + \frac{\pi}{2}\right)\right) + 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
=
0
$$0$$
product
/ ____________\ / ____________\
| / ___ | | / ___ |
-pi pi |\/ -1 + \/ 2 | |\/ -1 + \/ 2 |
0*----*--*-2*atan|---------------|*2*atan|---------------|
2 2 | ___________| | ___________|
| / ___ | | / ___ |
\ \/ 1 + \/ 2 / \ \/ 1 + \/ 2 /
$$\frac{\pi}{2} \cdot 0 \left(- \frac{\pi}{2}\right) \left(- 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}\right) 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
=
0
$$0$$
0
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
-pi
x2 = ----
2
$$x_{2} = - \frac{\pi}{2}$$
pi
x3 = --
2
$$x_{3} = \frac{\pi}{2}$$
/ ____________\
| / ___ |
|\/ -1 + \/ 2 |
x4 = -2*atan|---------------|
| ___________|
| / ___ |
\ \/ 1 + \/ 2 /
$$x_{4} = - 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
/ ____________\
| / ___ |
|\/ -1 + \/ 2 |
x5 = 2*atan|---------------|
| ___________|
| / ___ |
\ \/ 1 + \/ 2 /
$$x_{5} = 2 \operatorname{atan}{\left(\frac{\sqrt{-1 + \sqrt{2}}}{\sqrt{1 + \sqrt{2}}} \right)}$$
x5 = 2*atan(sqrt(-1 + sqrt(2))/sqrt(1 + sqrt(2)))
Numerical answer
[src]
x1 = -97.3893722612836
x2 = -43.9822971502571
x3 = -29.845130209103
x4 = -25.9181393921158
x5 = 28.2743338823081
x6 = 29.845130209103
x7 = -81.6814089933346
x8 = -15.707963267949
x9 = -55.7632696012188
x10 = 72.2566310325652
x11 = -39.2699081698724
x12 = 95.8185759344887
x13 = -257.610597594363
x14 = 45.553093477052
x15 = -53.4070751110265
x16 = -9.42477796076938
x17 = -87.1791961371168
x18 = 81.6814089933346
x19 = -11.7809724509617
x20 = 38.484510006475
x21 = -21.9911485751286
x22 = 76.1836218495525
x23 = -32.9867228626928
x24 = -14.1371669411541
x25 = 42.4115008234622
x26 = 69.9004365423729
x27 = -72.2566310325652
x28 = 32.2013246992954
x29 = 15.707963267949
x30 = 50.2654824574367
x31 = 68.329640215578
x32 = -28.2743338823081
x33 = -80.1106126665397
x34 = 102.101761241668
x35 = 63.6172512351933
x36 = -87.9645943005142
x37 = -18.0641577581413
x38 = -62.0464549083984
x39 = 48.6946861306418
x40 = -19.6349540849362
x41 = 0.0
x42 = 20.4203522483337
x43 = 89.5353906273091
x44 = 24.3473430653209
x45 = -65.9734457253857
x46 = 18.8495559215388
x47 = -73.8274273593601
x48 = 6.28318530717959
x49 = -36.1283155162826
x50 = 94.2477796076938
x51 = -61.261056745001
x52 = 65.9734457253857
x53 = 36.1283155162826
x54 = 21.9911485751286
x55 = 55.7632696012188
x56 = 78.5398163397448
x57 = -89.5353906273091
x58 = 4.71238898038469
x59 = 7.85398163397448
x60 = 14.1371669411541
x61 = -76.1836218495525
x62 = 86.3937979737193
x63 = 87.9645943005142
x64 = 12.5663706143592
x65 = 51.8362787842316
x66 = -37.6991118430775
x67 = 1156.10609652104
x68 = -51.8362787842316
x69 = -51.0508806208341
x70 = -69.9004365423729
x71 = -1.5707963267949
x72 = 59.6902604182061
x73 = -88.7499924639117
x74 = 64.4026493985908
x75 = 43.9822971502571
x76 = -63.6172512351933
x77 = 182.997772071605
x78 = -95.8185759344887
x79 = 80.1106126665397
x80 = -2400.1767873426
x81 = 73.8274273593601
x82 = -59.6902604182061
x83 = -7.85398163397448
x84 = 25.9181393921158
x85 = -86.3937979737193
x86 = 92.6769832808989
x87 = 18.0641577581413
x88 = -45.553093477052
x89 = -83.2522053201295
x90 = 62.0464549083984
x91 = 1.5707963267949
x92 = -58.1194640914112
x93 = 58.1194640914112
x94 = -94.2477796076938
x95 = -42.4115008234622
x96 = 34.5575191894877
x97 = -99.7455667514759
x98 = -57.3340659280137
x98 = -57.3340659280137