Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 6*x^2+x-7=0
-
Equation (x^2-9)^2+(x^2+x-6)^2=0
-
Equation (x-5)=(x+10)^2
-
Equation x^3+4*x^2+x-6=0
- Express {x} in terms of y where:
- 2*x+20*y=16
- 2*x+10*y=-5
- -19*x-20*y=1
- -9*x+11*y=-1
- Sum of series:
-
-1
- Derivative of:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- cos(- two *x)=- one
- co sinus of e of ( minus 2 multiply by x) equally minus 1
- co sinus of e of ( minus two multiply by x) equally minus one
- cos(-2x)=-1
- cos-2x=-1
-
Similar expressions
- cos(2*x)=-1
- -sin(x)+cos(-2*x+3*pi/2)=0
- cos^-2(x)=1
- 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 = 10.9955743696636
x2 = 39.2699084246933
x3 = -17.2787598091171
x4 = 54.9778711883962
x5 = -26.7035372990183
x6 = 48.6946859238715
x7 = 92.6769830795146
x8 = 1.5707965454425
x9 = 32.986722928111
x10 = 17.2787598502655
x11 = 4.71238876848081
x12 = 76.9690197631883
x13 = 39.2699081179815
x14 = -54.9778713137198
x15 = -86.393797765473
x16 = -14.1371668392726
x17 = 98.9601685932308
x18 = 26.7035373461441
x19 = -76.9690202568697
x20 = 10.9955740392793
x21 = -32.9867227513827
x22 = 17.2787595624179
x23 = 83.2522055730903
x24 = 70.6858345016621
x25 = -4.7123889912442
x26 = -42.4115006098842
x27 = -98.9601684414698
x28 = 51.8362788999928
x29 = 61.2610566752601
x30 = -51.8362786897497
x31 = -48.6946860920117
x32 = -61.2610569641117
x33 = -83.2522055415057
x34 = 83.2522052340866
x35 = -98.96016883042
x36 = -92.6769830239371
x37 = -39.2699083866483
x38 = 32.9867226137576
x39 = 64.4026493086922
x40 = 42.4115007291722
x41 = -67.5442421675773
x42 = -20.4203520321877
x43 = 61.2610569989704
x44 = 7.85398174058521
x45 = 80.1106126771746
x46 = -58.1194639993376
x47 = -92.6769831823972
x48 = 36.1283156002139
x49 = 541.924732890135
x50 = 80.1106131434937
x51 = -61.2610562242523
x52 = 54.9778714849733
x53 = -89.5353907467661
x54 = -76.9690198771149
x55 = 14.1371671048484
x56 = 45.553093700501
x57 = -73.8274272800405
x58 = -48.6946858738636
x59 = -23.5619450090417
x60 = -10.9955741902138
x61 = 20.4203521497111
x62 = -29.8451300963672
x63 = 58.1194644379895
x64 = -32.9867231091652
x65 = -95.8185758681287
x66 = 86.393797888273
x67 = 23.5619451230057
x68 = -7.85398149857354
x69 = -64.4026491876462
x70 = -70.685834448838
x71 = -98.960168684456
x72 = -10.9955745350309
x73 = 23.5619449395428
x74 = -26.7035375427973
x75 = 98.9601683381274
x76 = -39.2699081528781
x77 = -45.5530935883361
x78 = -36.1283154192437
x79 = -80.1106125795659
x80 = -17.2787590276524
x81 = 73.8274274795554
x82 = 67.5442422779275
x83 = -4.71238872430683
x84 = 76.9690200400775
x85 = -70.6858346386357
x86 = -54.9778716831146
x87 = 29.845130320338
x88 = 89.5353908552844
x89 = -1.57079642969308
x90 = 76.9690207492347
x91 = 95.8185760590309
x91 = 95.8185760590309