Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation sin^3(x)+sin(x)=sqrt(3)*cos^3(x)-2sqrt(3)*cos(x)
-
Equation x^4+x^2=0
-
Equation x-x/11=50/11
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Equation x²+(x+2)²=10²
- Express {x} in terms of y where:
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
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Identical expressions
- sin^ three (x)+sin(x)=sqrt(three)*cos^ three (x)-2sqrt(three)*cos(x)
- sinus of cubed (x) plus sinus of (x) equally square root of (3) multiply by co sinus of e of cubed (x) minus 2 square root of (3) multiply by co sinus of e of (x)
- sinus of to the power of three (x) plus sinus of (x) equally square root of (three) multiply by co sinus of e of to the power of three (x) minus 2 square root of (three) multiply by co sinus of e of (x)
- sin^3(x)+sin(x)=√(3)*cos^3(x)-2√(3)*cos(x)
- sin3(x)+sin(x)=sqrt(3)*cos3(x)-2sqrt(3)*cos(x)
- sin3x+sinx=sqrt3*cos3x-2sqrt3*cosx
- sin³(x)+sin(x)=sqrt(3)*cos³(x)-2sqrt(3)*cos(x)
- sin to the power of 3(x)+sin(x)=sqrt(3)*cos to the power of 3(x)-2sqrt(3)*cos(x)
- sin^3(x)+sin(x)=sqrt(3)cos^3(x)-2sqrt(3)cos(x)
- sin3(x)+sin(x)=sqrt(3)cos3(x)-2sqrt(3)cos(x)
- sin3x+sinx=sqrt3cos3x-2sqrt3cosx
- sin^3x+sinx=sqrt3cos^3x-2sqrt3cosx
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Similar expressions
- sin^3(x)+sin(x)=sqrt(3)*cos^3(x)+2sqrt(3)*cos(x)
- sin^3(x)-sin(x)=sqrt(3)*cos^3(x)-2sqrt(3)*cos(x)
- sin^3(x)+sinx=sqrt(3)*cos^3(x)-2sqrt(3)*cosx
sin^3(x)+sin(x)=sqrt(3)*cos^3(x)-2sqrt(3)*cos(x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3 ___ 3 ___ sin (x) + sin(x) = \/ 3 *cos (x) - 2*\/ 3 *cos(x)
$$\sin^{3}{\left(x \right)} + \sin{\left(x \right)} = \sqrt{3} \cos^{3}{\left(x \right)} - 2 \sqrt{3} \cos{\left(x \right)}$$
Rapid solution
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
/ / _____________\\ / / _____________\\
| | / ___ || | | / ___ ||
x3 = 2*im\atanh\\/ 3 + 2*\/ 2 // - 2*I*re\atanh\\/ 3 + 2*\/ 2 //
$$x_{3} = 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}$$
/ / _____________\\ / / _____________\\
| | / ___ || | | / ___ ||
x4 = - 2*im\atanh\\/ 3 + 2*\/ 2 // + 2*I*re\atanh\\/ 3 + 2*\/ 2 //
$$x_{4} = - 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}$$
/ _____________\
| / ___ |
x5 = -2*I*atanh\\/ 3 - 2*\/ 2 /
$$x_{5} = - 2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)}$$
/ _____________\
| / ___ |
x6 = 2*I*atanh\\/ 3 - 2*\/ 2 /
$$x_{6} = 2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)}$$
x6 = 2*i*atanh(sqrt(3 - 2*sqrt(2)))
Sum and product of roots
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sum
/ / _____________\\ / / _____________\\ / / _____________\\ / / _____________\\ / _____________\ / _____________\ pi 2*pi | | / ___ || | | / ___ || | | / ___ || | | / ___ || | / ___ | | / ___ | - -- + ---- + 2*im\atanh\\/ 3 + 2*\/ 2 // - 2*I*re\atanh\\/ 3 + 2*\/ 2 // + - 2*im\atanh\\/ 3 + 2*\/ 2 // + 2*I*re\atanh\\/ 3 + 2*\/ 2 // - 2*I*atanh\\/ 3 - 2*\/ 2 / + 2*I*atanh\\/ 3 - 2*\/ 2 / 3 3
$$\left(- 2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)} + \left(\left(\left(- \frac{\pi}{3} + \frac{2 \pi}{3}\right) + \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}\right)\right) + \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}\right)\right)\right) + 2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
/ / / _____________\\ / / _____________\\\ / / / _____________\\ / / _____________\\\ / _____________\ / _____________\ -pi 2*pi | | | / ___ || | | / ___ ||| | | | / ___ || | | / ___ ||| | / ___ | | / ___ | ----*----*\2*im\atanh\\/ 3 + 2*\/ 2 // - 2*I*re\atanh\\/ 3 + 2*\/ 2 ///*\- 2*im\atanh\\/ 3 + 2*\/ 2 // + 2*I*re\atanh\\/ 3 + 2*\/ 2 ///*-2*I*atanh\\/ 3 - 2*\/ 2 /*2*I*atanh\\/ 3 - 2*\/ 2 / 3 3
$$2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)} - 2 i \operatorname{atanh}{\left(\sqrt{3 - 2 \sqrt{2}} \right)} - \frac{\pi}{3} \frac{2 \pi}{3} \left(2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} - 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}\right) \left(- 2 \operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} + 2 i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}\right)$$
=
2
/ / / _____________\\ / / _____________\\\ / _____________\
2 | | | / ___ || | | / ___ ||| 2| / ___ |
32*pi *\- I*re\atanh\\/ 3 + 2*\/ 2 // + im\atanh\\/ 3 + 2*\/ 2 /// *atanh \\/ 3 - 2*\/ 2 /
------------------------------------------------------------------------------------------------
9
$$\frac{32 \pi^{2} \left(\operatorname{im}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)} - i \operatorname{re}{\left(\operatorname{atanh}{\left(\sqrt{2 \sqrt{2} + 3} \right)}\right)}\right)^{2} \operatorname{atanh}^{2}{\left(\sqrt{3 - 2 \sqrt{2}} \right)}}{9}$$
32*pi^2*(-i*re(atanh(sqrt(3 + 2*sqrt(2)))) + im(atanh(sqrt(3 + 2*sqrt(2)))))^2*atanh(sqrt(3 - 2*sqrt(2)))^2/9
Numerical answer
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x1 = -29.3215314335047
x2 = 71.2094334813686
x3 = 49.2182849062401
x4 = 118.333323285216
x5 = -82.7286065445312
x6 = -38.7463093942741
x7 = 90.0589894029074
x8 = 598.996999284454
x9 = -23.0383461263252
x10 = -48.1710873550435
x11 = 190.589954317781
x12 = -45.0294947014537
x13 = 93.2005820564972
x14 = 36.6519142918809
x15 = -7.33038285837618
x16 = -13.6135681655558
x17 = 20.943951023932
x18 = -1031.48958792865
x19 = -79.5870138909414
x20 = 86.9173967493176
x21 = 52.3598775598299
x22 = -73.3038285837618
x23 = -89.0117918517108
x24 = 55.5014702134197
x25 = 33.5103216382911
x26 = -16.7551608191456
x27 = -19.8967534727354
x28 = -76.4454212373516
x29 = 27.2271363311115
x30 = 80.634211442138
x31 = -85.870199198121
x32 = 96.342174710087
x33 = -63.8790506229925
x34 = -10.471975511966
x35 = 24.0855436775217
x36 = 58.6430628670095
x37 = 5.23598775598299
x38 = 30.3687289847013
x39 = 42.9350995990605
x40 = -35.6047167406843
x41 = 83.7758040957278
x42 = -101.57816246607
x43 = 39.7935069454707
x44 = -1.0471975511966
x45 = -54.4542726622231
x46 = 74.3510261349584
x47 = 14.6607657167524
x48 = -95.2949771588904
x49 = -60.7374579694027
x50 = 8.37758040957278
x51 = 64.9262481741891
x52 = 17.8023583703422
x53 = 11.5191730631626
x54 = -51.3126800086333
x55 = -26.1799387799149
x56 = -41.8879020478639
x57 = -67.0206432765823
x58 = -32.4631240870945
x59 = -98.4365698124802
x60 = 99.4837673636768
x61 = 77.4926187885482
x62 = -4.18879020478639
x63 = -57.5958653158129
x64 = -92.1533845053006
x65 = 68.0678408277789
x66 = 2.0943951023932
x67 = -117.286125734019
x68 = 46.0766922526503
x69 = 61.7846555205993
x70 = -70.162235930172
x70 = -70.162235930172