Mister Exam
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- Equation:
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Equation x+7*4=40
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Equation x^3=x^2+2x
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Equation 6x^2+x-7=0
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Equation 6x-14=1+3x
- Express {x} in terms of y where:
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Identical expressions
- sin(-x/ two)= one
- sinus of ( minus x divide by 2) equally 1
- sinus of ( minus x divide by two) equally one
- sin-x/2=1
- sin(-x divide by 2)=1
-
Similar expressions
- sin(x/2)=1
- sin-(x/2)=-1/2
sin(-x/2)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/-x \ sin|---| = 1 \ 2 /
$$\sin{\left(\frac{\left(-1\right) x}{2} \right)} = 1$$
Detail solution
Given the equation
$$\sin{\left(\frac{\left(-1\right) x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = -1$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \pi$$
$$x_{2} = 4 \pi n + 3 \pi$$
$$\sin{\left(\frac{\left(-1\right) x}{2} \right)} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = -1$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{2} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \pi$$
$$x_{2} = 4 \pi n + 3 \pi$$
Sum and product of roots
[src]
sum
-pi + 3*pi
$$- \pi + 3 \pi$$
=
2*pi
$$2 \pi$$
product
-pi*3*pi
$$- \pi 3 \pi$$
=
2 -3*pi
$$- 3 \pi^{2}$$
-3*pi^2
Numerical answer
[src]
x1 = -28.2743345506996
x2 = -53.4070760410661
x3 = -78.5398160355522
x4 = 47.123890256687
x5 = -15.7079641216365
x6 = -15.7079632966168
x7 = -28.2743329527591
x8 = 47.1238897245433
x9 = -53.407074099621
x10 = -65.9734467103803
x11 = 59.6902594160982
x12 = 47.1238893765929
x13 = -40.840702830856
x14 = -40.8407049390955
x15 = -3.14159244591793
x16 = 97.3893725976594
x17 = -78.5398173635881
x18 = -78.5398169064311
x19 = 97.3893712357817
x20 = 84.8230017459365
x21 = 9.42477828111644
x22 = 47.1238908281958
x23 = 34.5575201953822
x24 = -78.5398153571806
x25 = 34.5575198674508
x26 = 21.9911493543639
x27 = 84.8230026783574
x28 = -15.7079624977706
x29 = 59.6902606135717
x30 = -28.2743337045464
x31 = 9.42477785524033
x32 = -28.2743333728019
x33 = -91.1061864056832
x34 = 84.8230022236836
x35 = 34.5575190198289
x36 = 97.3893732551872
x37 = -53.4070755183111
x38 = -40.840705514174
x39 = -3.1415920909332
x40 = -53.4070752977589
x41 = 84.8230013528861
x42 = 21.9911476515378
x43 = -3.14159162121992
x44 = -65.9734466347336
x45 = -53.4070744460719
x46 = -65.9734464982309
x47 = -78.5398163457967
x48 = -40.8407034751919
x49 = 9.42477693583124
x50 = 59.6902591286344
x51 = 84.8230006713996
x52 = 47.1238887891963
x53 = -3.14159389871743
x54 = -3.14159296369468
x55 = 34.5575202880375
x56 = -65.9734448735059
x57 = 97.3893717230424
x58 = -28.2743348785101
x59 = 47.1238883520716
x60 = -40.8407040589859
x61 = 9.4247774082407
x62 = 34.5575182674959
x63 = -91.1061859213063
x64 = -28.2743336521146
x65 = -3.14159363499305
x66 = -40.8407043325125
x67 = 21.9911485852083
x68 = 72.2566318142828
x69 = -3.1415950208335
x70 = 59.6902613557236
x71 = -103.672556618325
x72 = 72.2566301889781
x73 = 21.9911494370191
x74 = 72.2566319571987
x75 = -15.7079623299946
x76 = -65.9734449211945
x77 = 72.2566310277173
x78 = 34.5575187273286
x79 = -15.7079640213661
x80 = 59.6902608771019
x81 = 97.3893735581761
x82 = -91.1061893000426
x83 = 9.42477894916069
x84 = 59.6902597628977
x85 = -91.1061879410652
x86 = -91.10618728017
x87 = 21.9911478139095
x88 = 47.123891242423
x89 = 72.2566302523232
x90 = -91.1061866269766
x91 = -103.672558275184
x92 = -40.8407057343968
x93 = -65.9734457649054
x93 = -65.9734457649054