Mister Exam
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How to use it?
- Equation:
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Equation 3x^2=0
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Equation x^4-7x^2+12=0
- Equation 9^x-26*3^x-27=0
- Equation 4x^2-100=0
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
-
Identical expressions
- cos^ two x-3sinxcosx+2sin^2x=2
- co sinus of e of squared x minus 3 sinus of x co sinus of e of x plus 2 sinus of squared x equally 2
- co sinus of e of to the power of two x minus 3 sinus of x co sinus of e of x plus 2 sinus of squared x equally 2
- cos2x-3sinxcosx+2sin2x=2
- cos²x-3sinxcosx+2sin²x=2
- cos to the power of 2x-3sinxcosx+2sin to the power of 2x=2
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Similar expressions
- cos^2x-3sinxcosx-2sin^2x=2
- cos^2x+3sinxcosx+2sin^2x=2
cos^2x-3sinxcosx+2sin^2x=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 2 cos (x) - 3*sin(x)*cos(x) + 2*sin (x) = 2
$$\left(- 3 \sin{\left(x \right)} \cos{\left(x \right)} + \cos^{2}{\left(x \right)}\right) + 2 \sin^{2}{\left(x \right)} = 2$$
Rapid solution
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
pi
x2 = --
2
$$x_{2} = \frac{\pi}{2}$$
/ ____\ x3 = 2*atan\3 - \/ 10 /
$$x_{3} = 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)}$$
/ ____\ x4 = 2*atan\3 + \/ 10 /
$$x_{4} = 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
x4 = 2*atan(3 + sqrt(10))
Sum and product of roots
[src]
sum
pi pi / ____\ / ____\ - -- + -- + 2*atan\3 - \/ 10 / + 2*atan\3 + \/ 10 / 2 2
$$\left(2 \operatorname{atan}{\left(3 - \sqrt{10} \right)} + \left(- \frac{\pi}{2} + \frac{\pi}{2}\right)\right) + 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
=
/ ____\ / ____\ 2*atan\3 + \/ 10 / + 2*atan\3 - \/ 10 /
$$2 \operatorname{atan}{\left(3 - \sqrt{10} \right)} + 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
product
-pi pi / ____\ / ____\ ----*--*2*atan\3 - \/ 10 /*2*atan\3 + \/ 10 / 2 2
$$- \frac{\pi}{2} \frac{\pi}{2} \cdot 2 \operatorname{atan}{\left(3 - \sqrt{10} \right)} 2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
=
2 / ____\ / ____\ -pi *atan\3 + \/ 10 /*atan\3 - \/ 10 /
$$- \pi^{2} \operatorname{atan}{\left(3 - \sqrt{10} \right)} \operatorname{atan}{\left(3 + \sqrt{10} \right)}$$
-pi^2*atan(3 + sqrt(10))*atan(3 - sqrt(10))
Numerical answer
[src]
x1 = 15.3862127135523
x2 = -64.4026493985908
x3 = -23.5619449019235
x4 = -29.845130209103
x5 = 42.4115008234622
x6 = -75.7199742405517
x7 = 4.71238898038469
x8 = -22.3128991295252
x9 = 36.1283155162826
x10 = -3.46334320798644
x11 = 18.5278053671421
x12 = -91.4279375085006
x13 = -17.2787595947439
x14 = 26.7035375555132
x15 = -6.60493586157623
x16 = 40.5189539422707
x17 = -80.1106126665397
x18 = 43.6605465958605
x19 = 86.3937979737193
x20 = -69.4367889333721
x21 = 39.2699081698724
x22 = 12.2446200599625
x23 = 64.4026493985908
x24 = -895.675656827488
x25 = -83.2522053201295
x26 = -95.8185759344887
x27 = -47.4456403582435
x28 = 71.9348804781686
x29 = -1.5707963267949
x30 = -16.0297138223456
x31 = -86.3937979737193
x32 = 73.8274273593601
x33 = -1864.53523990554
x34 = -39.2699081698724
x35 = -60.0120109726027
x36 = -72.5783815869619
x37 = 70.6858347057703
x38 = -0.321750554396642
x39 = -66.2951962797823
x40 = 65.651695170989
x41 = -42.4115008234622
x42 = 87.6428437461176
x43 = -51.8362787842316
x44 = 58.1194640914112
x45 = -73.8274273593601
x46 = 51.8362787842316
x47 = 93.9260290532972
x48 = 29.845130209103
x49 = -45.553093477052
x50 = 21.6693980207319
x51 = -31.7376770902946
x52 = 80.1106126665397
x53 = -58.1194640914112
x54 = -82.0031595477313
x55 = -36.1283155162826
x56 = 49.9437319030401
x57 = -50.5872330118333
x58 = -44.3040477046537
x59 = -25.454491783115
x60 = -67.5442420521806
x61 = 6417.95204072955
x62 = -9.74652851516602
x63 = 27.9525833279115
x64 = -7.85398163397448
x65 = 48.6946861306418
x66 = 34.2357686350911
x67 = 56.2269172102196
x68 = -97.7111228156802
x69 = 7.85398163397448
x70 = -14.1371669411541
x71 = -94.5695301620904
x72 = 78.2180657853482
x73 = -53.7288256654231
x74 = 100.209214360477
x75 = -38.0208623974742
x76 = 14.1371669411541
x77 = 5.96143475278294
x78 = 20.4203522483337
x79 = 95.8185759344887
x80 = -89.5353906273091
x81 = 62.5101025173992
x82 = 84.5012510925278
x83 = -88.2863448549109
x84 = 92.6769832808989
x85 = -61.261056745001
x86 = -28.5960844367048
x86 = -28.5960844367048