Mister Exam
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How to use it?
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Equation sin^3x+cos^3x=1
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Identical expressions
- sin^3x+cos^3x= one
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Similar expressions
- sin^3x-cos^3x=1
sin^3x+cos^3x=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3 3 sin (x) + cos (x) = 1
$$\sin^{3}{\left(x \right)} + \cos^{3}{\left(x \right)} = 1$$
Sum and product of roots
[src]
sum
pi / / ___\\ / / ___\\ / / ___\\ / / ___\\
0 + -- + - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 // + - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
2
$$\left(0\right) + \left(\frac{\pi}{2}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) + \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
pi / / ___\\ / / ___\\ / / ___\\ / / ___\\ -- - 2*re\atan\1 + I*\/ 2 // - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 // 2
$$- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} + \frac{\pi}{2} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
product
pi / / ___\\ / / ___\\ / / ___\\ / / ___\\
0 * -- * - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 // * - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
2
$$\left(0\right) * \left(\frac{\pi}{2}\right) * \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}\right) * \left(- 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}\right)$$
=
0
$$0$$
Rapid solution
[src]
x_1 = 0
$$x_{1} = 0$$
pi
x_2 = --
2
$$x_{2} = \frac{\pi}{2}$$
/ / ___\\ / / ___\\ x_3 = - 2*re\atan\1 - I*\/ 2 // - 2*I*im\atan\1 - I*\/ 2 //
$$x_{3} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 - \sqrt{2} i \right)}\right)}$$
/ / ___\\ / / ___\\ x_4 = - 2*re\atan\1 + I*\/ 2 // - 2*I*im\atan\1 + I*\/ 2 //
$$x_{4} = - 2 \operatorname{re}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)} - 2 i \operatorname{im}{\left(\operatorname{atan}{\left(1 + \sqrt{2} i \right)}\right)}$$
Numerical answer
[src]
x1 = 25.1327409724573
x2 = -92.6769829534337
x3 = -62.8318532927495
x4 = -62.8318531490441
x5 = -23.5619453892223
x6 = 62.8318527701137
x7 = 20.4203531255275
x8 = -10.9955741975213
x9 = 43.9822965618047
x10 = -42.411500559126
x11 = 12.5663704209738
x12 = -29.845130077235
x13 = 95.8185760776522
x14 = 37.6991119410686
x15 = 32.9867229085985
x16 = -86.3937977169853
x17 = -31.4159267385166
x18 = -75.3982238977935
x19 = 76.9690200083598
x20 = -94.2477795073904
x21 = -4.7123886543052
x22 = 6.28318528355781
x23 = -6.2831853710703
x24 = -67.5442421400044
x25 = -48.6946858034808
x26 = 56.5486675806638
x27 = 32.9867225841519
x28 = -61.2610564810716
x29 = -18.8495561616182
x30 = -54.9778716209105
x31 = 87.9645942607522
x32 = -37.6991118786703
x33 = 76.9690197103284
x34 = -111.526539371047
x35 = 37.6991120117423
x36 = -80.1106125702373
x37 = 51.8362789161893
x38 = 39.2699084940311
x39 = 94.2477796093488
x40 = -18.8495566567427
x41 = 1.57079659839545
x42 = 81.6814090975898
x43 = -69.1150386913156
x44 = -25.1327415380683
x45 = 26.7035376074808
x46 = 100.53096474054
x47 = 20.4203528971238
x48 = 345.575192215452
x49 = 70.6858347080917
x50 = -50.2654823569461
x51 = -43.982297175623
x52 = 58.1194648612742
x53 = -23.5619449859209
x54 = -81.6814090405953
x55 = -87.9645943648228
x56 = 83.2522056414558
x57 = 18.8495556157537
x58 = 87.9645943335328
x59 = 69.115038109091
x60 = 20.4203521688202
x61 = 7.8539817544154
x62 = 75.3982235745282
x63 = -36.128315407708
x64 = 50.2654824461838
x65 = -98.960168426996
x66 = -54.9778713095897
x67 = -73.8274272702661
x68 = 64.4026493241994
x69 = -6.28318520741857
x70 = -10.9955742573891
x71 = 81.6814090883321
x72 = 45.5530937555641
x73 = 32.9867221580314
x74 = 35380.6164645649
x75 = 0.0
x76 = -17.2787594636263
x77 = 64.4026493079487
x78 = 89.5353909123641
x79 = 43.9822971687748
x80 = -106.8141494103
x81 = 14.1371671334464
x81 = 14.1371671334464
The graph