Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x-3=10
-
Equation 4*x^4-5*x^2+1=0
-
Equation 5*x^2+7*x+2=0
-
Equation 3/8*x+15=1/6*x+10
- Express {x} in terms of y where:
- -2*x+4*y=3
- -14*x-13*y=11
- -1*x-5*y=-1
- -12*x-6*y=-3
- Integral of d{x}:
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cos(x/3)
-
-1
- Limit of the function:
-
cos(x/3)
- Derivative of:
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cos(x/3)
-
-1
- Sum of series:
-
-1
-
Identical expressions
- cos(x/ three)=- one
- co sinus of e of (x divide by 3) equally minus 1
- co sinus of e of (x divide by three) equally minus one
- cosx/3=-1
- cos(x divide by 3)=-1
-
Similar expressions
- 2cos^2x/3-5cosx/3-3=0
- cos(x/3)=+1
- cos(x)/3+1/3=1/3-cos(x)/3
- cos*x/3=-1
cos(x/3)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\frac{x}{3} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{3} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{3} = \pi n + \pi$$
$$\frac{x}{3} = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n + 3 \pi$$
$$x_{2} = 3 \pi n$$
$$\cos{\left(\frac{x}{3} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{3} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{3} = \pi n + \pi$$
$$\frac{x}{3} = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 3 \pi n + 3 \pi$$
$$x_{2} = 3 \pi n$$
Sum and product of roots
[src]
sum
3*pi
$$3 \pi$$
=
3*pi
$$3 \pi$$
product
3*pi
$$3 \pi$$
=
3*pi
$$3 \pi$$
3*pi
Numerical answer
[src]
x1 = 9.42477857411892
x2 = 28.2743324300573
x3 = 9.42477904486572
x4 = -28.2743337041057
x5 = -103.672556179644
x6 = 47.1238910361097
x7 = -47.1238882805255
x8 = -84.8230028759433
x9 = -28.2743345778791
x10 = -9.42477898962262
x11 = -65.9734470685728
x12 = 65.9734469290305
x13 = 65.9734466656459
x14 = -9.42477813943337
x15 = 28.2743323982258
x16 = -28.2743328502299
x17 = 28.2743304203258
x18 = -84.8230001004278
x19 = -47.1238909371531
x20 = -65.9734457649013
x21 = -28.2743352595136
x22 = -47.1238906645642
x23 = -28.2743328840357
x24 = 23495.9714577684
x25 = 47.1238898180831
x26 = 65.9734496550071
x27 = 47.1238882655668
x28 = 47.1238893703748
x29 = 65.9734457530057
x30 = 84.82300316301
x31 = -65.9734441237693
x32 = 84.8230013509188
x33 = -47.1238870896323
x34 = 9.42477739402688
x35 = 28.2743329655993
x36 = -84.8230015302339
x37 = -84.8230021042216
x38 = -84.8230012105749
x39 = -28.2743353334451
x40 = -47.1238885000614
x41 = 65.9734449275366
x42 = -47.1238913434704
x43 = 84.8230001090646
x44 = 84.8230005314505
x45 = -84.8230014829494
x46 = 65.9734442942041
x47 = -47.1238892339559
x48 = 9.42477909729197
x49 = 103.672556103604
x50 = -65.9734448054309
x51 = -65.9734442370237
x52 = 9.42477950690576
x53 = -28.274332356029
x54 = 47.1238902640918
x55 = -65.973444487036
x56 = -9.42478044884868
x57 = 9.42477644878639
x58 = 28.2743353277095
x59 = 65.9734443589411
x60 = 28.2743347048405
x61 = 103.672556203947
x62 = -65.9734465446611
x63 = -9.42477649339056
x64 = -47.1238903314038
x65 = 47.1238897836275
x66 = -9.4247794819084
x67 = -9.42477658006982
x68 = 84.8230010300176
x69 = -84.8230031826845
x70 = 84.823000552695
x71 = 65.9734472216308
x72 = -9.424778905987
x73 = 84.8230022399184
x74 = 65.973449200012
x75 = 9.42477666029867
x76 = -65.9734471669578
x77 = -47.1238901244433
x78 = 47.1238885910376
x79 = -9.42477726195834
x80 = -28.2743310539003
x81 = 47.123891348278
x82 = -28.2743342852867
x83 = -84.8230004308799
x84 = 9.42477828364719
x85 = 28.2743326778891
x86 = -103.672556133526
x87 = 28.2743352495238
x88 = -216.769897336347
x89 = 84.8230029651094
x90 = -103.672561360559
x91 = 103.672560042967
x92 = 28.2743338651733
x92 = 28.2743338651733
The graph