Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 81*x^3+18*x^2+x=0
-
Equation 6=8-5(7x-1)
-
Equation 3x=28-x
-
Equation 3x=2
- Express {x} in terms of y where:
- -13*x-7*y=16
- -16*x+10*y=-11
- -2*x-15*y=-1
- -14*x+5*y=-1
-
Identical expressions
- one two cosx- six *(three)^(1/2)= zero
- 12 co sinus of e of x minus 6 multiply by (3) to the power of (1 divide by 2) equally 0
- one two co sinus of e of x minus six multiply by (three) to the power of (1 divide by 2) equally zero
- 12cosx-6*(3)(1/2)=0
- 12cosx-6*31/2=0
- 12cosx-6(3)^(1/2)=0
- 12cosx-6(3)(1/2)=0
- 12cosx-631/2=0
- 12cosx-63^1/2=0
- 12cosx-6*(3)^(1/2)=O
- 12cosx-6*(3)^(1 divide by 2)=0
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Similar expressions
- 12cosx+6*(3)^(1/2)=0
12cosx-6*(3)^(1/2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$12 \cos{\left(x \right)} - 6 \sqrt{3} = 0$$
- this is the simplest trigonometric equation
We get:
$$12 \cos{\left(x \right)} = 6 \sqrt{3}$$
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
$$12 \cos{\left(x \right)} - 6 \sqrt{3} = 0$$
- this is the simplest trigonometric equation
Move -6*sqrt(3) to right part of the equation
with the change of sign in -6*sqrt(3)
We get:
$$12 \cos{\left(x \right)} = 6 \sqrt{3}$$
Divide both parts of the equation by 12
The equation is transformed to
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Or
$$x = \pi n + \frac{\pi}{6}$$
$$x = \pi n - \frac{5 \pi}{6}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
11*pi
x2 = -----
6
$$x_{2} = \frac{11 \pi}{6}$$
x2 = 11*pi/6
Sum and product of roots
[src]
sum
pi 11*pi -- + ----- 6 6
$$\frac{\pi}{6} + \frac{11 \pi}{6}$$
=
2*pi
$$2 \pi$$
product
pi 11*pi --*----- 6 6
$$\frac{\pi}{6} \frac{11 \pi}{6}$$
=
2 11*pi ------ 36
$$\frac{11 \pi^{2}}{36}$$
11*pi^2/36
Numerical answer
[src]
x1 = 100.007366139275
x2 = -82.2050077689329
x3 = 69.6386371545737
x4 = 68.5914396033772
x5 = -12.0427718387609
x6 = 19.3731546971371
x7 = 6.80678408277789
x8 = -18.3259571459405
x9 = -43.4586983746588
x10 = 44.5058959258554
x11 = 0.523598775598299
x12 = 87.4409955249159
x13 = -100.007366139275
x14 = 74.8746249105567
x15 = 12.0427718387609
x16 = 57.0722665402146
x17 = 94.7713783832921
x18 = -93.7241808320955
x19 = 37.1755130674792
x20 = 88.4881930761125
x21 = 75.9218224617533
x22 = 30.8923277602996
x23 = 81.1578102177363
x24 = 93.7241808320955
x25 = 62.3082542961976
x26 = 82.2050077689329
x27 = 56.025068989018
x28 = 18.3259571459405
x29 = -75.9218224617533
x30 = -31.9395253114962
x31 = -101.054563690472
x32 = 63.3554518473942
x33 = -87.4409955249159
x34 = 13.0899693899575
x35 = -56.025068989018
x36 = -6.80678408277789
x37 = 25.6563400043166
x38 = -69.6386371545737
x39 = -49.7418836818384
x40 = -44.5058959258554
x41 = -94.7713783832921
x42 = -25.6563400043166
x43 = -5.75958653158129
x44 = -50.789081233035
x45 = -13.0899693899575
x46 = 38.2227106186758
x47 = -88.4881930761125
x48 = 31.9395253114962
x49 = -68.5914396033772
x50 = -81.1578102177363
x51 = -37.1755130674792
x52 = -0.523598775598299
x53 = -62.3082542961976
x54 = 49.7418836818384
x55 = 24.60914245312
x56 = 5.75958653158129
x57 = -24.60914245312
x58 = 1168.1488683598
x59 = -63.3554518473942
x60 = -38.2227106186758
x61 = 43.4586983746588
x62 = -74.8746249105567
x63 = 194.255145746969
x64 = 50.789081233035
x65 = -4028.04538067771
x66 = -57.0722665402146
x67 = -30.8923277602996
x68 = -19.3731546971371
x68 = -19.3731546971371