Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation x^2-2x=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
- Canonical form:
- cos(x+(pi/6))
- Sum of series:
-
-1
- Derivative of:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- cos(x+(pi/ six))=- one
- co sinus of e of (x plus ( Pi divide by 6)) equally minus 1
- co sinus of e of (x plus ( Pi divide by six)) equally minus one
- cosx+pi/6=-1
- cos(x+(pi divide by 6))=-1
-
Similar expressions
- cos(x-(pi/6))=-1
- cos(x+(pi/6))=+1
- cos(x+pi/6)=sqrt(1)
cos(x+(pi/6))=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x + \frac{\pi}{6} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n + \pi$$
$$x + \frac{\pi}{6} = \pi n$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
$$\cos{\left(x + \frac{\pi}{6} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n + \pi$$
$$x + \frac{\pi}{6} = \pi n$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
Sum and product of roots
[src]
sum
5*pi ---- 6
$$\frac{5 \pi}{6}$$
=
5*pi ---- 6
$$\frac{5 \pi}{6}$$
product
5*pi ---- 6
$$\frac{5 \pi}{6}$$
=
5*pi ---- 6
$$\frac{5 \pi}{6}$$
5*pi/6
Numerical answer
[src]
x1 = 46.6002915424766
x2 = -41.3643034756348
x3 = 90.5825886559265
x4 = 2.6179943910887
x5 = -60.2138592131301
x6 = -97.9129706275257
x7 = -66.4970442260639
x8 = 84.2994025838914
x9 = -22.5147478349319
x10 = -60.2138597029021
x11 = 15.1843640805114
x12 = 34.033920359193
x13 = 34.0339207847038
x14 = 8.90117965615139
x15 = -66.4970449881741
x16 = 84.2994028380602
x17 = 78.0162179198714
x18 = -3.66519167007196
x19 = 46.6002908409077
x20 = -361.80675444881
x21 = 27.7507352698553
x22 = 15.1843648857238
x23 = 2.61799455496506
x24 = 34.0339199446972
x25 = 52.8834768102045
x26 = 52.8834760280739
x27 = -192.160751677378
x28 = 96.8657739641184
x29 = 90.582587999292
x30 = -3.66519092743494
x31 = -9.94837719937213
x32 = 27.7507349796545
x33 = -72.7802294264824
x34 = -22.5147470684883
x35 = 71.7330320678828
x36 = -1008.97484129336
x37 = 59.1666609764865
x38 = 27.7507345972419
x39 = 59.1666620416755
x40 = -990.125283913897
x41 = -9.94837684361999
x42 = 59.1666612361331
x43 = -53.9306743428435
x44 = -35.0811182860801
x45 = -53.9306741059445
x46 = 78.016217089327
x47 = 8.90117887095619
x48 = -85.346599517262
x49 = -60.2138590484297
x50 = -16.2315621141929
x51 = -91.629785915216
x52 = -72.7802302304008
x53 = -53.9306734890854
x54 = -35.0811178580174
x55 = -79.0634144072739
x56 = 78.0162175421798
x57 = -85.3465999122838
x58 = -91.6297852224741
x59 = 40.317106219532
x60 = 128.281701088874
x61 = -47.6474887938562
x62 = 40.317105455911
x63 = 71.7330324287761
x64 = 71.7330317476983
x65 = 90.5825886936576
x66 = -16.2315625529615
x67 = 46.6002916014283
x68 = -41.3643024840352
x69 = 96.8657731852716
x70 = -97.9129718332953
x71 = 21.4675493184699
x72 = 65.4498472464142
x73 = -79.0634146523615
x74 = -22.5147473714457
x75 = -9.94837635164697
x76 = -3.665191483537
x77 = -47.6474880747764
x78 = 8.90117807116979
x79 = 84.2994033661045
x80 = -79.0634154430337
x81 = -97.9129714856759
x82 = -91.6297858037994
x83 = -66.4970455792652
x84 = -85.3466006337956
x85 = -41.3643027605
x86 = -35.0811174980382
x87 = -16.2315618892079
x88 = -28.7979330750006
x89 = 2.61799368259923
x90 = 65.4498464720272
x91 = -28.7979322703294
x92 = 21.4675500890045
x93 = 40.3171056770577
x94 = -47.6474886438032
x94 = -47.6474886438032
The graph