Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation cos(x)+sin(x)=0
-
Equation 7+x=4
- Express {x} in terms of y where:
- 7*x-2*y=20
- -7*x-7*y=-14
- -15*x+17*y=13
- 20*x+4*y=-7
- Graphing y =:
- cosx-1
-
Identical expressions
- cosx- one = zero
- co sinus of e of x minus 1 equally 0
- co sinus of e of x minus one equally zero
- cosx-1=O
-
Similar expressions
- cosx+1=0
- sqrt(3)/2*cos(x)-1/2*sin(x)=cos3x
- 2*sqrt(3)*sin((x+pi)/3)-cos(2*x)=3*cos(x)-1
- sqrt(cos(x)-1)=0
cosx-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(x \right)} = 1$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$x = \pi n$$
$$x = \pi n - \pi$$
, where n - is a integer
$$\cos{\left(x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move -1 to right part of the equation
with the change of sign in -1
We get:
$$\cos{\left(x \right)} = 1$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Or
$$x = \pi n$$
$$x = \pi n - \pi$$
, where n - is a integer
Sum and product of roots
[src]
sum
2*pi
$$2 \pi$$
=
2*pi
$$2 \pi$$
product
0*2*pi
$$0 \cdot 2 \pi$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 18.8495556275525
x2 = 37.6991113348642
x3 = 62.8318527849002
x4 = 12.5663710110881
x5 = -94.2477801171671
x6 = 43.9822971694647
x7 = -50.2654829667315
x8 = -94.2477794452815
x9 = 56.5486680806249
x10 = 81.6814084860076
x11 = 12.5663711301703
x12 = 6.28318528420851
x13 = 6.28318626747926
x14 = -87.964593928489
x15 = -81.6814075578313
x16 = 56.5486676011951
x17 = -50.265482641087
x18 = 81.6814085860518
x19 = 43.9822974733639
x20 = 81.6814091897036
x21 = -56.5486674685864
x22 = -62.8318534787248
x23 = -69.1150379045123
x24 = 37.6991120311338
x25 = -81.6814092565354
x26 = 31.4159268459961
x27 = -87.9645947692094
x28 = -62.831852673202
x29 = -69.1150386869085
x30 = -18.8495555173448
x31 = 25.1327416384075
x32 = -43.9822967932182
x33 = 100.530964759815
x34 = 12.5663704426592
x35 = 94.2477796093523
x36 = -75.3982231045728
x37 = 31.4159260648825
x38 = 6.28318500093652
x39 = 87.9645938121814
x40 = -6.2831858160515
x41 = -4.79511606158654e-7
x42 = -81.6814084945807
x43 = -25.1327407505866
x44 = -12.5663703112531
x45 = 3.40772025642919e-7
x46 = 37.6991115173992
x47 = -18.8495552124105
x48 = 0.0
x49 = -75.3982231720141
x50 = 18.8495564031971
x51 = 50.2654824463392
x52 = -75.3982238741744
x53 = 50.2654821322586
x54 = -81.6814090382277
x55 = -43.9822971745392
x56 = -56.5486682426592
x57 = 75.3982232188727
x58 = -87.9645943586158
x59 = 94.2477800892631
x60 = 25.1327408328211
x61 = -37.6991121287155
x62 = 50.2654829439723
x63 = 69.1150379887504
x64 = 43.9822966661001
x65 = 6.28318579821791
x66 = 69.115038794053
x67 = -6.2831851275477
x68 = -94.2477797298079
x69 = -43.9822976246252
x70 = 56.5486668532011
x71 = -12.5663710889626
x72 = -50.2654822863493
x73 = -25.1327415297174
x74 = -31.4159260208155
x75 = 62.8318535568358
x76 = 56.5486682809363
x77 = 94.2477792651059
x78 = -31.4159267157965
x79 = -6.28318555849548
x80 = -18.8495563230046
x81 = 87.964594335905
x82 = 87.9645946044253
x83 = -37.6991118772631
x84 = -31.4159260507536
x85 = 75.3982240031607
x86 = -37.6991113479743
x87 = -100.530964626003
x88 = 100.530965157364
x88 = 100.530965157364
The graph