Mister Exam
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How to use it?
- Equation:
- Equation a^2*x^2-21*a^2+a*x+1=0
-
Equation 12-y+2=0
-
Equation 2*cos(x)=1
-
Equation 7x-(3+2x)=x+9
- Express {x} in terms of y where:
- -5*x+15*y=-15
- 5*x+18*y=15
- -12*x+2*y=14
- -6*x-6*y=0
- Derivative of:
-
3sinx+2cosx
-
Identical expressions
- 3sinx+2cosx= zero
- 3 sinus of x plus 2 co sinus of e of x equally 0
- 3 sinus of x plus 2 co sinus of e of x equally zero
- 3sinx+2cosx=O
-
Similar expressions
- 3sinx-2cosx=0
3sinx+2cosx=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3*sin(x) + 2*cos(x) = 0
$$3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$
Detail solution
Given the equation
$$3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$
transform:
$$\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -2$$
or
$$3 \tan{\left(x \right)} = -2$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = \frac{2}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{2}{3} \right)}$$
, where n - is a integer
$$3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} = 0$$
transform:
$$\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -2$$
or
$$3 \tan{\left(x \right)} = -2$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 3
The equation is transformed to
$$\tan{\left(x \right)} = \frac{2}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{2}{3} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-atan(2/3)
$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$
=
-atan(2/3)
$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$
product
-atan(2/3)
$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$
=
-atan(2/3)
$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$
-atan(2/3)
Rapid solution
[src]
x1 = -atan(2/3)
$$x_{1} = - \operatorname{atan}{\left(\frac{2}{3} \right)}$$
x1 = -atan(2/3)
Numerical answer
[src]
x1 = -72.8446336361128
x2 = -88.5525969040618
x3 = 81.0934063897871
x4 = -13.1543732179067
x5 = -25.7207438322659
x6 = -97.9773748648312
x7 = -79.1278189432924
x8 = -57.1366703681638
x9 = -47.7118924073945
x10 = -60.2782630217536
x11 = -6.87118791072715
x12 = -10.0127805643169
x13 = 37.11110923953
x14 = 15.1199606644014
x15 = -211.074710394064
x16 = -53.9950777145741
x17 = 65.3854431218381
x18 = -0.588002603547568
x19 = -44.5702997538047
x20 = -3.72959525713736
x21 = 46.5358872002993
x22 = -82.2694115968822
x23 = -22.5791511786761
x24 = 74.8102210826075
x25 = 2006.88970304033
x26 = -32.0039291394455
x27 = 2.55359005004223
x28 = -94.8357822112414
x29 = -91.6941895576516
x30 = 5.69518270363202
x31 = 11.9783680108116
x32 = 27.6863312787606
x33 = -69.703040982523
x34 = 96.801369657736
x35 = 43.3942945467095
x36 = 30.8279239323504
x37 = -41.4287071002149
x38 = 77.9518137361973
x39 = 21.403145971581
x40 = 18.2615533179912
x41 = 33.9695165859402
x42 = 87.3765916969666
x43 = 99.9429623113258
x44 = -19.4375585250863
x45 = 24.5447386251708
x46 = 93.6597770041462
x47 = 62.2438504682483
x48 = -50.8534850609843
x49 = 118.792518232865
x50 = 84.2349990433768
x51 = 90.5181843505564
x52 = 55.9606651610687
x53 = -75.9862262897026
x54 = 49.6774798538891
x55 = -28.8623364858557
x56 = -38.2871144466251
x57 = -85.411004250472
x58 = 417.243820323895
x59 = -66.5614483289332
x60 = 59.1022578146585
x61 = -35.1455217930353
x62 = 68.5270357754279
x63 = 52.8190725074789
x64 = 8.83677535722181
x65 = 40.2527018931197
x66 = -16.2959658714965
x67 = 71.6686284290177
x68 = -63.4198556753434
x69 = -101.118967518421
x69 = -101.118967518421