Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+11*x+30=0
-
Equation (-2-4t-1)²+(0+2t-1)²+(2+5t)²=9
-
Equation 1/3*x=12
-
Equation (|3*x-9|)-(|x+2|)=7
- Express {x} in terms of y where:
- 8*x-13*y=16
- -14*x+13*y=7
- -17*x-8*y=-8
- 12*x-15*y=0
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
- Derivative of:
-
-1
-
Identical expressions
- Sin(one / three *x)=- one
- Sin(1 divide by 3 multiply by x) equally minus 1
- Sin(one divide by three multiply by x) equally minus one
- Sin(1/3x)=-1
- Sin1/3x=-1
- Sin(1 divide by 3*x)=-1
-
Similar expressions
- Sin(1/3*x)=+1
Sin(1/3*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(\frac{x}{3} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{3} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{3 \pi}{2}$$
$$x_{2} = 6 \pi n + \frac{9 \pi}{2}$$
$$\sin{\left(\frac{x}{3} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{3} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{3} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$\frac{x}{3} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{3} = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{3}$$
we get the answer:
$$x_{1} = 6 \pi n - \frac{3 \pi}{2}$$
$$x_{2} = 6 \pi n + \frac{9 \pi}{2}$$
Sum and product of roots
[src]
sum
3*pi 9*pi - ---- + ---- 2 2
$$- \frac{3 \pi}{2} + \frac{9 \pi}{2}$$
=
3*pi
$$3 \pi$$
product
-3*pi 9*pi -----*---- 2 2
$$- \frac{3 \pi}{2} \frac{9 \pi}{2}$$
=
2 -27*pi ------- 4
$$- \frac{27 \pi^{2}}{4}$$
-27*pi^2/4
Rapid solution
[src]
-3*pi
x1 = -----
2
$$x_{1} = - \frac{3 \pi}{2}$$
9*pi
x2 = ----
2
$$x_{2} = \frac{9 \pi}{2}$$
x2 = 9*pi/2
Numerical answer
[src]
x1 = 32.986722548861
x2 = -80.1106089100043
x3 = 89.5353892972875
x4 = -42.4114992857075
x5 = -23.5619434738021
x6 = 32.9867224232349
x7 = -4.71238859426546
x8 = 51.8362823163449
x9 = -80.1106134301082
x10 = -42.4114997427582
x11 = 14.1371682432467
x12 = -42.4115021671282
x13 = -42.4114988767471
x14 = -80.1106140804049
x15 = 51.8362773664247
x16 = -4.71239024216915
x17 = 89.5353891331438
x18 = -4.71238845524301
x19 = -23.5619461984625
x20 = 70.6858336375702
x21 = 89.5353908982368
x22 = -42.4114999779636
x23 = 14.1371678181509
x24 = -80.1106140658652
x25 = 70.6858353577546
x26 = 14.1371654793596
x27 = -80.110611523969
x28 = 51.8362797759315
x29 = 51.8362780425465
x30 = -61.2610552425571
x31 = 89.5353917263916
x32 = 14.1371671114619
x33 = 70.6858329020223
x34 = 32.9867243978937
x35 = -23.5619482920391
x36 = -4.71238743209195
x37 = -42.4115023072805
x38 = 89.5353914041279
x39 = -23.5619434901217
x40 = 70.6858338911042
x41 = 14.1371656532869
x42 = 32.9867233840103
x43 = -42.411501460893
x44 = 51.8362773818419
x45 = -61.261055404731
x46 = 183.783173900171
x47 = 70.6858344740862
x48 = -4.71238948689267
x49 = 32.9867241354141
x50 = -98.9601689835803
x51 = 32.986722491348
x52 = 70.6858360595363
x53 = 14.1371660778537
x54 = -4.71238861603651
x55 = -23.5619458805467
x56 = 32.9867213216468
x57 = -61.2610570017434
x58 = -61.2610582551732
x59 = 14.1371684115644
x60 = -80.1106116945809
x61 = 89.5353922692829
x62 = 89.5353921684403
x63 = -23.56194501223
x64 = 51.8362798839346
x65 = -61.2610578317089
x66 = -23.5619441460216
x67 = -4.71239050808881
x68 = 51.8362802985196
x69 = -61.2610574882809
x70 = 70.6858361981262
x71 = -287.45572872034
x72 = -98.9601670486134
x73 = 32.9867216931265
x74 = -98.9601680902976
x75 = -61.2610582787117
x76 = 14.1371665638329
x77 = -23.5619464082898
x78 = -80.1106111588322
x79 = -61.2610561157384
x80 = 89.5353900126591
x81 = -98.960167330773
x82 = -23.5619459803956
x83 = -4.71238779907246
x84 = 70.6858331755052
x85 = -42.4115005778798
x86 = -98.9601688529851
x87 = -80.1106125777448
x88 = 51.8362789040765
x88 = 51.8362789040765