Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x+9=13-x
-
Equation x^2+4x+13=0
-
Equation log(x)-3+1/x=0
-
Equation x+6(3-3x)=35
- Express {x} in terms of y where:
- 2*x+13*y=-7
- -4*x-1*y=-6
- -7*x-1*y=7
- -20*x+17*y=-16
- Derivative of:
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cos(4*x)
-
-1
- Integral of d{x}:
-
cos(4*x)
-
-1
- Limit of the function:
-
cos(4*x)
- Sum of series:
-
-1
-
Identical expressions
- cos(four *x)=- one
- co sinus of e of (4 multiply by x) equally minus 1
- co sinus of e of (four multiply by x) equally minus one
- cos(4x)=-1
- cos4x=-1
-
Similar expressions
- (8*(sin(2x)^4))+(5*cos(4x))=3
- x^3+64=cos(4x)-2sin(4x)
- cos(4*x)=+1
cos(4*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(4 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$4 x = \pi n + \pi$$
$$4 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{4}$$
$$\cos{\left(4 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$4 x = \pi n + \pi$$
$$4 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{4}$$
Sum and product of roots
[src]
sum
pi -- 4
$$\frac{\pi}{4}$$
=
pi -- 4
$$\frac{\pi}{4}$$
product
pi -- 4
$$\frac{\pi}{4}$$
=
pi -- 4
$$\frac{\pi}{4}$$
pi/4
Numerical answer
[src]
x1 = 54.1924733267788
x2 = 76.1836219127145
x3 = 52.6216768417318
x4 = -18.0641577028072
x5 = 93.462381626966
x6 = -79.325214568582
x7 = 60.4756584745212
x8 = 41.6261027663993
x9 = -0.785398166130751
x10 = -5.49778725647941
x11 = -10.210176008893
x12 = 85.6083999066255
x13 = 55.7632697213615
x14 = 47.9092880382216
x15 = 91.8915851975093
x16 = -40.0553062838236
x17 = 63.6172513369298
x18 = -13.3517688688202
x19 = 10.2101761577675
x20 = 74.6128254135616
x21 = -33.7721211587531
x22 = -55.763269590985
x23 = 77.7544182976932
x24 = -16.4933615591447
x25 = 84.0376034192262
x26 = 27.4889354808973
x27 = 82.4668070519044
x28 = -41.6261027314388
x29 = 33.7721211448164
x30 = -63.6172513104641
x31 = -465.741111003319
x32 = 2.35619442704144
x33 = -71.4712329855388
x34 = 3.92699087784889
x35 = -76.1836217409515
x36 = 11.7809725680634
x37 = -19.6349541522704
x38 = 0.785398118063847
x39 = -11.780972425667
x40 = -85.608399889346
x41 = 38.4845098973237
x42 = -32.2013245860493
x43 = -24.3473429491357
x44 = -99.7455667547305
x45 = -57.3340660035604
x46 = -84.0376034471411
x47 = -38.4845100906754
x48 = 69.9004366179912
x49 = -98.1747705479865
x50 = -33.7721210085549
x51 = -46.3384915220366
x52 = 25.918139458182
x53 = -93.4623815613976
x54 = -60.4756586297418
x55 = 19.6349541951516
x56 = -54.1924731634027
x57 = 71.4712325592813
x58 = -3.92699105526517
x59 = 30.6305282706443
x60 = 90.3207887457625
x61 = -77.7544181730257
x62 = 98.1747704999445
x63 = -27.4889358330644
x64 = -49.4800844094223
x65 = 62.0464548185713
x66 = 18.0641575853046
x67 = 44.7676955973049
x68 = 46.3384915861013
x69 = -98.1747703186947
x70 = 40.055306209136
x71 = -2.35619437671896
x72 = -90.3207886690967
x73 = 99.7455668738049
x74 = 66.7588441131007
x75 = 24.347343006498
x76 = -82.4668071752083
x77 = 49.4800839996026
x78 = 68.3296401658547
x79 = 5.49778696422816
x80 = 96.6039739860399
x81 = 8.63937970041344
x82 = -62.0464548652478
x83 = 32.2013247418649
x84 = -68.3296400953708
x85 = 88.7499926302988
x86 = -35.3429174368834
x87 = 22.7765470504813
x88 = -19.6349539733882
x89 = 16.4933613203203
x89 = 16.4933613203203
The graph