Mister Exam
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How to use it?
- Equation:
- Equation sin5xcos3x-cos5xsin3x=-(sqrt(3)/2)
- Equation (399+601):k=625:25
-
Equation 20*x^2-21*x+22=17x^2-75x-218
-
Equation tg(3x+(pi)/6)=1
- 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
-
Identical expressions
- sin5xcos three x-cos5xsin3x=-(sqrt(3)/ two)
- sinus of 5x co sinus of e of 3x minus co sinus of e of 5x sinus of 3x equally minus ( square root of (3) divide by 2)
- sinus of 5x co sinus of e of three x minus co sinus of e of 5x sinus of 3x equally minus ( square root of (3) divide by two)
- sin5xcos3x-cos5xsin3x=-(√(3)/2)
- sin5xcos3x-cos5xsin3x=-sqrt3/2
- sin5xcos3x-cos5xsin3x=-(sqrt(3) divide by 2)
-
Similar expressions
- sin(3x)=-sqrt3/2
- sint=-sqrt3/2
- sin2x=-(sqrt3/2)
- sin5xcos3x+cos5xsin3x=-(sqrt(3)/2)
- sin(0.5x)=-sqrt3/2
- sin5xcos3x-cos5xsin3x=+(sqrt(3)/2)
sin5xcos3x-cos5xsin3x=-(sqrt(3)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
sin(5*x)*cos(3*x) - cos(5*x)*sin(3*x) = -------
2
$$- \sin{\left(3 x \right)} \cos{\left(5 x \right)} + \sin{\left(5 x \right)} \cos{\left(3 x \right)} = - \frac{\sqrt{3}}{2}$$
Sum and product of roots
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sum
pi pi 2*pi /log(2) / ___\\ 5*pi /log(2) / ___\\ - -- - -- + ---- + I*|------ - log\\/ 2 /| + ---- + I*|------ - log\\/ 2 /| 3 6 3 \ 2 / 6 \ 2 /
$$\left(\left(- \frac{\pi}{3} - \frac{\pi}{6}\right) + \left(\frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)\right) + \left(\frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$
=
/log(2) / ___\\
pi + 2*I*|------ - log\\/ 2 /|
\ 2 /
$$\pi + 2 i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
product
-pi -pi /2*pi /log(2) / ___\\\ /5*pi /log(2) / ___\\\ ----*----*|---- + I*|------ - log\\/ 2 /||*|---- + I*|------ - log\\/ 2 /|| 3 6 \ 3 \ 2 // \ 6 \ 2 //
$$- \frac{\pi}{3} \left(- \frac{\pi}{6}\right) \left(\frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right) \left(\frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)\right)$$
=
4 5*pi ----- 162
$$\frac{5 \pi^{4}}{162}$$
5*pi^4/162
Rapid solution
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-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
-pi
x2 = ----
6
$$x_{2} = - \frac{\pi}{6}$$
2*pi /log(2) / ___\\
x3 = ---- + I*|------ - log\\/ 2 /|
3 \ 2 /
$$x_{3} = \frac{2 \pi}{3} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
5*pi /log(2) / ___\\
x4 = ---- + I*|------ - log\\/ 2 /|
6 \ 2 /
$$x_{4} = \frac{5 \pi}{6} + i \left(- \log{\left(\sqrt{2} \right)} + \frac{\log{\left(2 \right)}}{2}\right)$$
x4 = 5*pi/6 + i*(-log(sqrt(2)) + log(2)/2)
Numerical answer
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x1 = -53.9306738866248
x2 = 96.342174710087
x3 = -57.5958653158129
x4 = -69.6386371545737
x5 = -25.6563400043166
x6 = -31.9395253114962
x7 = -13.6135681655558
x8 = -29.3215314335047
x9 = 80.634211442138
x10 = -88.4881930761125
x11 = -89.0117918517108
x12 = -41.8879020478639
x13 = -47.6474885794452
x14 = -45.0294947014537
x15 = 8.37758040957278
x16 = 34.0339204138894
x17 = -0.523598775598299
x18 = -28.7979326579064
x19 = -19.8967534727354
x20 = -242.426233102012
x21 = -91.6297857297023
x22 = -9.94837673636768
x23 = 71.2094334813686
x24 = 64.9262481741891
x25 = -66.497044500984
x26 = 36.6519142918809
x27 = 78.0162175641465
x28 = 30.3687289847013
x29 = 58.6430628670095
x30 = 8.90117918517108
x31 = 21.4675497995303
x32 = 24.0855436775217
x33 = -23.0383461263252
x34 = -82.2050077689329
x35 = -63.8790506229925
x36 = -16.7551608191456
x37 = 14.6607657167524
x38 = 87.4409955249159
x39 = 62.3082542961976
x40 = 2.0943951023932
x41 = -60.7374579694027
x42 = -85.870199198121
x43 = 46.0766922526503
x44 = -97.9129710368819
x45 = 86.9173967493176
x46 = -22.5147473507269
x47 = 18.3259571459405
x48 = 43.4586983746588
x49 = 42.9350995990605
x50 = 20.943951023932
x51 = -50.789081233035
x52 = -79.5870138909414
x53 = 124.616508592395
x54 = 74.3510261349584
x55 = -75.9218224617533
x56 = 65.4498469497874
x57 = -44.5058959258554
x58 = 37.1755130674792
x59 = -94.7713783832921
x60 = -1.0471975511966
x61 = -38.2227106186758
x62 = 68.5914396033772
x63 = 100.007366139275
x64 = -4.18879020478639
x65 = 15.1843644923507
x66 = 12.0427718387609
x67 = -95.2949771588904
x68 = -3.66519142918809
x69 = 68.0678408277789
x70 = -6.80678408277789
x71 = -261.799387799149
x72 = -73.3038285837618
x73 = 40.317105721069
x74 = 5.75958653158129
x75 = 84.2994028713261
x76 = 27.7507351067098
x77 = -16.2315620435473
x78 = -7.33038285837618
x79 = 90.0589894029074
x80 = 71.733032256967
x81 = 93.7241808320955
x82 = -35.6047167406843
x83 = -60.2138591938044
x84 = -67.0206432765823
x85 = 49.7418836818384
x86 = 56.025068989018
x87 = 52.3598775598299
x88 = -72.7802298081635
x89 = -51.3126800086333
x89 = -51.3126800086333