Mister Exam
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How to use it?
- Equation:
-
Equation (x+2)/9=(x-3)/2
-
Equation 11+2x=55+3x
-
Equation (x-2)^4+3*(x-2)^2-10=0
-
Equation 3*x^2-18=0
- Express {x} in terms of y where:
- 2*x+3*y=14
- 18*x-8*y=-2
- 16*x-7*y=-5
- 10*x-16*y=-6
-
Identical expressions
- 3sin(x)+4cos(x)= zero
- 3 sinus of (x) plus 4 co sinus of e of (x) equally 0
- 3 sinus of (x) plus 4 co sinus of e of (x) equally zero
- 3sinx+4cosx=0
- 3sin(x)+4cos(x)=O
-
Similar expressions
- 3sin(x)-4cos(x)=0
- 3sinx+4cosx=0
3sin(x)+4cos(x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3*sin(x) + 4*cos(x) = 0
$$3 \sin{\left(x \right)} + 4 \cos{\left(x \right)} = 0$$
Detail solution
Given the equation
$$3 \sin{\left(x \right)} + 4 \cos{\left(x \right)} = 0$$
transform:
$$\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -4$$
or
$$3 \tan{\left(x \right)} = -4$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = \frac{4}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{4}{3} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{4}{3} \right)}$$
, where n - is a integer
$$3 \sin{\left(x \right)} + 4 \cos{\left(x \right)} = 0$$
transform:
$$\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -4$$
or
$$3 \tan{\left(x \right)} = -4$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 3
The equation is transformed to
$$\tan{\left(x \right)} = \frac{4}{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{4}{3} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{4}{3} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-atan(4/3)
$$- \operatorname{atan}{\left(\frac{4}{3} \right)}$$
=
-atan(4/3)
$$- \operatorname{atan}{\left(\frac{4}{3} \right)}$$
product
-atan(4/3)
$$- \operatorname{atan}{\left(\frac{4}{3} \right)}$$
=
-atan(4/3)
$$- \operatorname{atan}{\left(\frac{4}{3} \right)}$$
-atan(4/3)
Rapid solution
[src]
x1 = -atan(4/3)
$$x_{1} = - \operatorname{atan}{\left(\frac{4}{3} \right)}$$
x1 = -atan(4/3)
Numerical answer
[src]
x1 = 55.6213725466147
x2 = 58.7629652002045
x3 = -26.06003644672
x4 = 2.21429743558818
x5 = 36.7718166250759
x6 = -41.7679997146689
x7 = -4.06888787159141
x8 = 83.8957064289228
x9 = 87.0372990825126
x10 = 39.9134092786657
x11 = -44.9095923682587
x12 = 33.6302239714861
x13 = -70.0423335969771
x14 = 65.046150507384
x15 = 99.6036696968718
x16 = 46.1965945858453
x17 = -16.6352584859506
x18 = -10.352073178771
x19 = 96.462077043282
x20 = -35.4848144074893
x21 = -73.1839262505669
x22 = -22.9184437931302
x23 = -98.3166674792852
x24 = -92.0334821721056
x25 = -32.3432217538995
x26 = 8.49748274276777
x27 = 52.4797798930249
x28 = -85.750296864926
x29 = -60.6175556362077
x30 = -54.3343703290281
x31 = 93.3204843896922
x32 = -48.0511850218485
x33 = 14.7806680499474
x34 = -13.4936658323608
x35 = -0.927295218001612
x36 = -57.4759629826179
x37 = 49.3381872394351
x38 = -38.6264070610791
x39 = 61.9045578537943
x40 = -63.7591482897975
x41 = 80.754113775333
x42 = 90.1788917361024
x43 = -88.8918895185158
x44 = 24.2054460107167
x45 = -7.2104805251812
x46 = 27.3470386643065
x47 = -51.1927776754383
x48 = -710.927234929295
x49 = -66.9007409433873
x50 = 109.028447657641
x51 = 11.6390753963576
x52 = 71.3293358145636
x53 = -29.2016291003098
x54 = -19.7768511395404
x55 = 21.0638533571269
x56 = 168.718708075847
x57 = -79.4671115577464
x58 = -95.1750748256954
x59 = 68.1877431609738
x60 = 5.35589008917797
x61 = 74.4709284681534
x62 = -76.3255189041567
x63 = -82.6087042113362
x64 = 17.9222607035371
x65 = 30.4886313178963
x66 = 77.6125211217432
x67 = 43.0550019322555
x67 = 43.0550019322555