Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation cos(x)-1=0
- Equation 64-x^2=0
-
Equation sin(5*x)=-1
-
Equation cos(x/2)=-1
- Express {x} in terms of y where:
- 10*x-15*y=-2
- 16*x-9*y=4
- -9*x-20*y=14
- 13*x+12*y=-18
- Derivative of:
-
cos(x/2)
-
-1
- Graphing y =:
- cos(x/2)
- Limit of the function:
-
cos(x/2)
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- cos(x/ two)=- one
- co sinus of e of (x divide by 2) equally minus 1
- co sinus of e of (x divide by two) equally minus one
- cosx/2=-1
- cos(x divide by 2)=-1
-
Similar expressions
- cos(x/2-п/7)=√3/2
- cos(x/2)=+1
- (cosx*cosx*cosx)/(2sinx)=1
cos(x/2)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(\frac{x}{2} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{2} = \pi n + \pi$$
$$\frac{x}{2} = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + 2 \pi$$
$$x_{2} = 2 \pi n$$
$$\cos{\left(\frac{x}{2} \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{x}{2} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Or
$$\frac{x}{2} = \pi n + \pi$$
$$\frac{x}{2} = \pi n$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + 2 \pi$$
$$x_{2} = 2 \pi n$$
Sum and product of roots
[src]
sum
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
product
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
2*pi
Numerical answer
[src]
x1 = 94.2477796093523
x2 = -69.1150393645777
x3 = -6.28318597231491
x4 = 6.28318445599649
x5 = 56.5486668446775
x6 = -81.6814098544517
x7 = -69.115038701061
x8 = 81.6814094388795
x9 = 94.2477803922665
x10 = -18.8495569383691
x11 = -18.8495548993085
x12 = -81.6814090382823
x13 = 69.115037955532
x14 = -31.4159274639505
x15 = -69.1150380827831
x16 = -56.548667456373
x17 = -31.4159267991785
x18 = -31.4159269573538
x19 = 94.2477787666659
x20 = 81.681409932803
x21 = 18.8495564877336
x22 = 69.115038835587
x23 = 31.4159259869291
x24 = -56.5486687887842
x25 = 18.8495549415754
x26 = 43.9822980146158
x27 = -6.28318512498487
x28 = -81.6814082319334
x29 = -56.5486683277755
x30 = 18.8495569537229
x31 = 31.4159268602638
x32 = 18.8495554920234
x33 = -94.2477794433785
x34 = 56.5486684458067
x35 = 81.6814069775521
x36 = 69.1150397628024
x37 = 973.893720162307
x38 = 6.28318454684724
x39 = 69.1150373651011
x40 = 81.6814091930517
x41 = 56.5486675992574
x42 = -56.5486667805662
x43 = 6.28318624191326
x44 = -420.973417050673
x45 = -69.1150405916551
x46 = -6.28318437561383
x47 = -18.8495554800568
x48 = -94.2477802857943
x49 = -18.8495563601837
x50 = 6.28318608026041
x51 = 56.5486672894687
x52 = -18.8495572113627
x53 = -69.115037346238
x54 = -31.4159267183799
x55 = -81.68140804614
x56 = 18.8495556154405
x57 = 43.9822963919738
x58 = 56.5486681672153
x59 = -43.9822979202134
x60 = 94.2477805288104
x61 = -31.4159258676764
x62 = -69.1150378269834
x63 = -43.9822971745293
x64 = -6.28318500560576
x65 = -94.2477786842917
x66 = 81.6814083413212
x67 = -94.2477790629797
x68 = 31.4159255107699
x69 = -6.28318630492991
x70 = -56.5486677946696
x71 = -81.6814097251289
x72 = 94.2477788210844
x73 = -43.9822963521153
x74 = 69.1150368714384
x75 = 43.9822979229286
x76 = -94.2477805989545
x77 = 43.9822962232996
x78 = 69.1150394039813
x79 = 18.8495561010751
x80 = -43.9822980632848
x81 = -6.28318627375063
x82 = 43.982297169474
x83 = -43.982296295854
x84 = -18.8495543136467
x85 = -6.28318480992034
x86 = 31.415926404003
x87 = 31.4159275256971
x88 = -31.4159255258029
x89 = 81.6814079898679
x90 = 56.548668769019
x91 = 6.28318528419795
x91 = 6.28318528419795
The graph