Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+4*x+4=0
-
Equation 90+x-4*10=60
-
Equation 6*3+x=72
-
Equation x^3+x^2=0
- Express {x} in terms of y where:
- -4*x+19*y=-13
- -5*x-6*y=-1
- -16*x-2*y=4
- -7*x+15*y=18
- Graphing y =:
- cos(2*x)
- Derivative of:
-
cos(2*x)
-
-1
- Integral of d{x}:
- cos(2*x)
-
-1
- Sum of series:
-
-1
-
Identical expressions
- cos(two *x)=- one
- co sinus of e of (2 multiply by x) equally minus 1
- co sinus of e of (two multiply by x) equally minus one
- cos(2x)=-1
- cos2x=-1
-
Similar expressions
- cos2x=1/2
- (cosx*cos2x)/(tgx-1)=0
- cos(2*x)=+1
cos(2*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(2 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$2 x = \pi n + \pi$$
$$2 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{2}$$
$$x_{2} = \frac{\pi n}{2}$$
$$\cos{\left(2 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$2 x = \pi n + \pi$$
$$2 x = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{2}$$
$$x_{2} = \frac{\pi n}{2}$$
Sum and product of roots
[src]
sum
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
pi -- 2
$$\frac{\pi}{2}$$
=
pi -- 2
$$\frac{\pi}{2}$$
pi/2
Numerical answer
[src]
x1 = -61.2610569641117
x2 = -4.71238872430683
x3 = -45.5530935883361
x4 = 54.9778714849733
x5 = 20.4203521497111
x6 = -1.57079642969308
x7 = 67.5442422779275
x8 = -4.7123889912442
x9 = -10.9955745350309
x10 = -7.85398149857354
x11 = 32.9867226137576
x12 = 32.986722928111
x13 = 39.2699081179815
x14 = 541.924732890135
x15 = 7.85398174058521
x16 = 10.9955743696636
x17 = 17.2787598502655
x18 = -10.9955741902138
x19 = -92.6769831823972
x20 = 45.553093700501
x21 = -80.1106125795659
x22 = -64.4026491876462
x23 = 73.8274274795554
x24 = -23.5619450090417
x25 = 61.2610569989704
x26 = 76.9690207492347
x27 = -51.8362786897497
x28 = 4.71238876848081
x29 = -61.2610562242523
x30 = -95.8185758681287
x31 = -70.685834448838
x32 = -76.9690202568697
x33 = 61.2610566752601
x34 = 70.6858345016621
x35 = -26.7035372990183
x36 = -39.2699081528781
x37 = -54.9778716831146
x38 = -58.1194639993376
x39 = 17.2787595624179
x40 = 76.9690200400775
x41 = -89.5353907467661
x42 = -98.960168684456
x43 = 54.9778711883962
x44 = 36.1283156002139
x45 = 92.6769830795146
x46 = 76.9690197631883
x47 = 89.5353908552844
x48 = -98.96016883042
x49 = 98.9601685932308
x50 = -26.7035375427973
x51 = 86.393797888273
x52 = 80.1106131434937
x53 = -32.9867231091652
x54 = 51.8362788999928
x55 = 95.8185760590309
x56 = -36.1283154192437
x57 = -48.6946860920117
x58 = -83.2522055415057
x59 = 23.5619451230057
x60 = 23.5619449395428
x61 = -17.2787590276524
x62 = -20.4203520321877
x63 = 58.1194644379895
x64 = 10.9955740392793
x65 = -67.5442421675773
x66 = 29.845130320338
x67 = -76.9690198771149
x68 = -29.8451300963672
x69 = -98.9601684414698
x70 = -70.6858346386357
x71 = 80.1106126771746
x72 = -14.1371668392726
x73 = 1.5707965454425
x74 = 39.2699084246933
x75 = -48.6946858738636
x76 = -54.9778713137198
x77 = -92.6769830239371
x78 = 42.4115007291722
x79 = 64.4026493086922
x80 = -73.8274272800405
x81 = 98.9601683381274
x82 = -42.4115006098842
x83 = 26.7035373461441
x84 = -39.2699083866483
x85 = 83.2522052340866
x86 = 83.2522055730903
x87 = -17.2787598091171
x88 = 14.1371671048484
x89 = 48.6946859238715
x90 = -32.9867227513827
x91 = -86.393797765473
x91 = -86.393797765473
The graph