Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -x^2-4*x-3=0
-
Equation cos(x)=-3
-
Equation sin(-x)=0
-
Equation (x+3)^3=81*(x+3)
- Express {x} in terms of y where:
- -15*x+9*y=18
- 19*x-1*y=9
- -1*x-19*y=-7
- -19*x-4*y=17
-
Identical expressions
- sin(-x/ three)+ one = two
- sinus of ( minus x divide by 3) plus 1 equally 2
- sinus of ( minus x divide by three) plus one equally two
- sin-x/3+1=2
- sin(-x divide by 3)+1=2
-
Similar expressions
- sin(x/3)+1=2
- sin(-x/3)-1=2
sin(-x/3)+1=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/-x \ sin|---| + 1 = 2 \ 3 /
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} + 1 = 2$$
Detail solution
Given the equation
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} + 1 = 2$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\frac{x}{3} \right)} = -1$$
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:
$$x_{1} = 6 \pi n - \frac{3 \pi}{2}$$
$$x_{2} = 6 \pi n + \frac{9 \pi}{2}$$
$$\sin{\left(\frac{\left(-1\right) x}{3} \right)} + 1 = 2$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1
The equation is transformed to
$$\sin{\left(\frac{x}{3} \right)} = -1$$
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 = 32.9867213216468
x2 = -80.110611523969
x3 = -98.9601670486134
x4 = -4.71238859426546
x5 = -98.9601680902976
x6 = -61.2610578317089
x7 = -4.71238779907246
x8 = -4.71238861603651
x9 = 14.1371665638329
x10 = -98.9601688529851
x11 = -61.2610570017434
x12 = 51.8362773818419
x13 = -80.1106125777448
x14 = 51.8362802985196
x15 = -98.9601689835803
x16 = -4.71238743209195
x17 = -23.5619464082898
x18 = -4.71238948689267
x19 = 32.9867243978937
x20 = 32.9867233840103
x21 = 51.8362789040765
x22 = 89.5353900126591
x23 = 32.9867216931265
x24 = -42.4114999779636
x25 = -61.2610552425571
x26 = -23.5619458805467
x27 = -80.1106111588322
x28 = -23.5619434901217
x29 = -80.1106116945809
x30 = -23.5619434738021
x31 = 14.1371656532869
x32 = 70.6858360595363
x33 = 51.8362773664247
x34 = 183.783173900171
x35 = -42.4115023072805
x36 = -4.71239050808881
x37 = -287.45572872034
x38 = 14.1371671114619
x39 = -61.2610582551732
x40 = 32.986722491348
x41 = 14.1371682432467
x42 = -42.4114988767471
x43 = 32.9867224232349
x44 = 32.986722548861
x45 = 89.5353917263916
x46 = -23.5619459803956
x47 = 14.1371684115644
x48 = 89.5353892972875
x49 = 14.1371678181509
x50 = -4.71239024216915
x51 = -23.56194501223
x52 = 89.5353922692829
x53 = -61.2610574882809
x54 = -80.1106134301082
x55 = 70.6858353577546
x56 = -61.2610582787117
x57 = 70.6858338911042
x58 = 89.5353908982368
x59 = 14.1371654793596
x60 = -80.1106089100043
x61 = 51.8362823163449
x62 = -80.1106140658652
x63 = 70.6858331755052
x64 = -42.4115021671282
x65 = 89.5353891331438
x66 = 14.1371660778537
x67 = 32.9867241354141
x68 = 70.6858336375702
x69 = -98.960167330773
x70 = -23.5619482920391
x71 = -42.4115005778798
x72 = 70.6858344740862
x73 = 89.5353914041279
x74 = 70.6858329020223
x75 = 51.8362798839346
x76 = -23.5619441460216
x77 = -42.4114992857075
x78 = 51.8362797759315
x79 = 89.5353921684403
x80 = -61.2610561157384
x81 = -42.4114997427582
x82 = -61.261055404731
x83 = -23.5619461984625
x84 = 51.8362780425465
x85 = -80.1106140804049
x86 = -4.71238845524301
x87 = 70.6858361981262
x88 = -42.411501460893
x88 = -42.411501460893