Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 11x-9=4x+19
-
Equation cos(x)=sqrt(3)/2
-
Equation 2*cos(x)+1=0
-
Equation x^4=(4*x-21)^2
- Express {x} in terms of y where:
- -6*x+1*y=14
- -8*x-12*y=15
- 9*x+8*y=6
- -6*x-2*y=-10
- Derivative of:
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cos(x)
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sqrt(3)/2
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
- Limit of the function:
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sqrt(3)/2
-
Identical expressions
- cos(x)=sqrt(three)/ two
- co sinus of e of (x) equally square root of (3) divide by 2
- co sinus of e of (x) equally square root of (three) divide by two
- cos(x)=√(3)/2
- cosx=sqrt3/2
- cos(x)=sqrt(3) divide by 2
-
Similar expressions
- 3sin^2x-7sinx×cosx+2cos^2x=0
- sqrt(((2-sqrt(3))/2)*(1+cos(x)))+sin(x)=1
- 4sqrt((1-((sqrt(3))/2))/(6x+6))+pi/(6x+6)=1,5*sqrt(3)-2
- cosx=sqrt(3)/2
cos(x)=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
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
$$\cos{\left(x \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
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 = -49.7418836818384
x2 = -87.4409955249159
x3 = 87.4409955249159
x4 = 93.7241808320955
x5 = -74.8746249105567
x6 = 30.8923277602996
x7 = 194.255145746969
x8 = -68.5914396033772
x9 = -38.2227106186758
x10 = -88.4881930761125
x11 = -100.007366139275
x12 = 88.4881930761125
x13 = -56.025068989018
x14 = 43.4586983746588
x15 = 94.7713783832921
x16 = 63.3554518473942
x17 = -101.054563690472
x18 = -43.4586983746588
x19 = 69.6386371545737
x20 = 50.789081233035
x21 = -19.3731546971371
x22 = -62.3082542961976
x23 = 56.025068989018
x24 = 62.3082542961976
x25 = -30.8923277602996
x26 = 57.0722665402146
x27 = 44.5058959258554
x28 = -25.6563400043166
x29 = -12.0427718387609
x30 = 82.2050077689329
x31 = 38.2227106186758
x32 = -0.523598775598299
x33 = -81.1578102177363
x34 = -13.0899693899575
x35 = -57.0722665402146
x36 = -93.7241808320955
x37 = 75.9218224617533
x38 = -50.789081233035
x39 = -37.1755130674792
x40 = 13.0899693899575
x41 = 6.80678408277789
x42 = 31.9395253114962
x43 = -31.9395253114962
x44 = 49.7418836818384
x45 = 18.3259571459405
x46 = 81.1578102177363
x47 = 24.60914245312
x48 = 68.5914396033772
x49 = 0.523598775598299
x50 = -69.6386371545737
x51 = 74.8746249105567
x52 = -63.3554518473942
x53 = -6.80678408277789
x54 = -75.9218224617533
x55 = 12.0427718387609
x56 = 25.6563400043166
x57 = -82.2050077689329
x58 = 5.75958653158129
x59 = -44.5058959258554
x60 = -24.60914245312
x61 = 19.3731546971371
x62 = 1168.1488683598
x63 = 37.1755130674792
x64 = 100.007366139275
x65 = -5.75958653158129
x66 = -18.3259571459405
x67 = -94.7713783832921
x67 = -94.7713783832921
The graph