Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 3x=2
-
Equation x^2+7x=18
-
Equation x^2-4x=0
-
Equation (y^4+4*y^2-12)/4=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- -7*x-19*y=-18
- 5*x+12*y=18
- -12*x-8*y=13
- Integral of d{x}:
-
cosx/1+2sinx
- Derivative of:
-
cosx/1+2sinx
-
Identical expressions
- cosx/ one +2sinx
- co sinus of e of x divide by 1 plus 2 sinus of x
- co sinus of e of x divide by one plus 2 sinus of x
- cosx divide by 1+2sinx
-
Similar expressions
- cosx/1-2sinx
cosx/1+2sinx equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
cos(x) ------ + 2*sin(x) = 0 1
$$2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1} = 0$$
Detail solution
Given the equation
$$2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1} = 0$$
transform:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$2 \tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$2 \sin{\left(x \right)} + \frac{\cos{\left(x \right)}}{1} = 0$$
transform:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
or
$$2 \tan{\left(x \right)} = -1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\tan{\left(x \right)} = \frac{1}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
0 - atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)} + 0$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
product
1*-atan(1/2)
$$1 \left(- \operatorname{atan}{\left(\frac{1}{2} \right)}\right)$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
-atan(1/2)
Numerical answer
[src]
x1 = 12.1027230053584
x2 = -100.994612523874
x3 = -22.4547961841294
x4 = -91.5698345631048
x5 = 5.81953769817878
x6 = -94.7114272166946
x7 = 65.5097981163849
x8 = -97.8530198702844
x9 = -41.3043521056681
x10 = 8.96113035176857
x11 = -72.7202786415661
x12 = 2.67794504458899
x13 = 43.5186495412563
x14 = 84.3593540379236
x15 = 835.199998245884
x16 = -44.4459447592579
x17 = 49.8018348484359
x18 = 191.173504259977
x19 = -47.5875374128477
x20 = -6.74683291618039
x21 = -141.835317020542
x22 = 21.5275009661277
x23 = -16.1716108769498
x24 = 81.2177613843338
x25 = -69.5786859879763
x26 = 37.2354642340767
x27 = -35.0211667984885
x28 = -19.3132035305396
x29 = 96.9257246522828
x30 = 52.9434275020257
x31 = -31.8795741448987
x32 = 93.784131998693
x33 = -79.0034639487456
x34 = -82.1450566023354
x35 = -88.428241909515
x36 = -0.463647609000806
x37 = 27.8106862733073
x38 = 30.9522789268971
x39 = -85.2866492559252
x40 = -50.7291300664375
x41 = 40.3770568876665
x42 = 34.0938715804869
x43 = 62.3682054627951
x44 = 15.2443156589482
x45 = 24.6690936197175
x46 = -28.7379814913089
x47 = 71.7929834235644
x48 = 87.5009466915134
x49 = 68.6513907699746
x50 = -60.1539080272069
x51 = 100.067317305873
x52 = -25.5963888377192
x53 = 46.6602421948461
x54 = 90.6425393451032
x55 = -9.88842556977019
x56 = -63.2955006807967
x57 = 18.385908312538
x58 = -66.4370933343865
x59 = 78.076168730744
x60 = -3.6052402625906
x61 = -57.0123153736171
x62 = -53.8707227200273
x63 = 56.0850201556155
x64 = -75.8618712951559
x65 = -13.03001822336
x66 = -38.1627594520783
x67 = -286.348579085672
x68 = 74.9345760771542
x69 = 59.2266128092053
x69 = 59.2266128092053
The graph