Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation 1-5*x=-6*x+8
-
Equation 10*(x-9)=7
-
Equation cos(x)=3
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-4*y=-20
- -9*x-15*y=-4
- 18*x-11*y=2
-
Identical expressions
- two sin3x+5cos3x=2
- 2 sinus of 3x plus 5 co sinus of e of 3x equally 2
- two sinus of 3x plus 5 co sinus of e of 3x equally 2
-
Similar expressions
- 2sin3x-5cos3x=2
2sin3x+5cos3x=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*sin(3*x) + 5*cos(3*x) = 2
$$2 \sin{\left(3 x \right)} + 5 \cos{\left(3 x \right)} = 2$$
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
-2*atan(3/7)
x2 = ------------
3
$$x_{2} = - \frac{2 \operatorname{atan}{\left(\frac{3}{7} \right)}}{3}$$
x2 = -2*atan(3/7)/3
Sum and product of roots
[src]
sum
pi 2*atan(3/7) -- - ----------- 6 3
$$- \frac{2 \operatorname{atan}{\left(\frac{3}{7} \right)}}{3} + \frac{\pi}{6}$$
=
2*atan(3/7) pi
- ----------- + --
3 6
$$- \frac{2 \operatorname{atan}{\left(\frac{3}{7} \right)}}{3} + \frac{\pi}{6}$$
product
pi -2*atan(3/7) --*------------ 6 3
$$\frac{\pi}{6} \left(- \frac{2 \operatorname{atan}{\left(\frac{3}{7} \right)}}{3}\right)$$
=
-pi*atan(3/7)
--------------
9
$$- \frac{\pi \operatorname{atan}{\left(\frac{3}{7} \right)}}{9}$$
-pi*atan(3/7)/9
Numerical answer
[src]
x1 = 18.5796280640154
x2 = -12.0427718387609
x3 = 130.376095123976
x4 = -27.4970641886349
x5 = -33.7802494958145
x6 = 42.4115008234622
x7 = 36.1283155162826
x8 = 34.0339204138894
x9 = -5.75958653158129
x10 = 65.4498469497874
x11 = 3.918862347263
x12 = 86.3937979737193
x13 = -65.1961760317125
x14 = -95.8185759344887
x15 = -1087.26098599959
x16 = 98.1666419549568
x17 = -1.5707963267949
x18 = 49.9955545999133
x19 = -18.3259571459405
x20 = 71.733032256967
x21 = -60.2138591938044
x22 = 1.82446724486981
x23 = 16.4852329616222
x24 = 10.2020476544426
x25 = 73.8274273593601
x26 = 31.9395253114962
x27 = 47.9011594975201
x28 = 100.26103705735
x29 = 78.0162175641465
x30 = 84.2994028713261
x31 = -93.7241808320955
x32 = 14.390837859229
x33 = -3.66519142918809
x34 = -69.3849662364988
x35 = -35.8746445982077
x36 = -62.3082542961976
x37 = -56.025068989018
x38 = -51.8362787842316
x39 = 91.8834566477772
x40 = 58.3731350094861
x41 = 163.886416762268
x42 = 27.7507351067098
x43 = -45.553093477052
x44 = 29.845130209103
x45 = 75.9218224617533
x46 = -31.6858543934213
x47 = 80.1106126665397
x48 = -58.1194640914112
x49 = 8.10765255204939
x50 = -49.7418836818384
x51 = 12.2964427568358
x52 = -100.007366139275
x53 = -29.5914592910281
x54 = -9.94837673636768
x55 = -97.9129710368819
x56 = 38.2227106186758
x57 = 69.6386371545737
x58 = 6.0132574496562
x59 = 45.8067643951269
x60 = -77.7625466460716
x61 = -42.1578299053873
x62 = -75.6681515436784
x63 = -7.85398163397448
x64 = 82.2050077689329
x65 = 62.5619252142725
x66 = -71.479361338892
x67 = -37.9690397006009
x68 = -84.0457319532512
x69 = 96.0722468525636
x70 = -14.1371669411541
x71 = 25.6563400043166
x72 = -53.9306738866248
x73 = -171.216799620644
x74 = -25.4026690862417
x75 = -40.0634348029941
x76 = -73.5737564412852
x77 = 19.3731546971371
x78 = -91.6297857297023
x79 = 556.839169379067
x80 = -16.2315620435473
x81 = -86.1401270556444
x82 = 40.317105721069
x83 = 56.2787399070929
x84 = 89.789061545384
x85 = 60.4675301118793
x86 = -89.5353906273091
x87 = -47.6474885794452
x88 = -79.8569417484648
x89 = -21.2138788814553
x90 = 93.9778517501704
x91 = 52.0899497023065
x92 = -81.951336850858
x93 = 21.4675497995303
x94 = 54.1843448046997
x94 = 54.1843448046997