Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation tan(x)=0
-
Equation log(4/(7-x))/log(x^2)=5
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Equation x-2(3x+2)=16
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Equation (7x+1)-(9x+3)=5
- Express {x} in terms of y where:
- (x^2+y^2-1)^3-x^2*y^3=0
- -2*x+1*y=-8
- -2*x-1*y=-8
- 4*x+15*y=19
- Integral of d{x}:
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cosx
- Derivative of:
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cosx
- Graphing y =:
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cosx
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Identical expressions
- cosx= three ^ zero . five / two
- co sinus of e of x equally 3 to the power of 0.5 divide by 2
- co sinus of e of x equally three to the power of zero . five divide by two
- cosx=30.5/2
- cosx=3^0.5 divide by 2
-
Similar expressions
- cos(x)=3/4
- cos(x+(п/3))*cos(x-(п/3))=-1/2
cosx=3^0.5/2 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
Sum and product of roots
[src]
sum
pi 11*pi
0 + -- + -----
6 6
$$\left(0 + \frac{\pi}{6}\right) + \frac{11 \pi}{6}$$
=
2*pi
$$2 \pi$$
product
pi 11*pi 1*--*----- 6 6
$$\frac{11 \pi}{6} \cdot 1 \frac{\pi}{6}$$
=
2 11*pi ------ 36
$$\frac{11 \pi^{2}}{36}$$
11*pi^2/36
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
11*pi
x2 = -----
6
$$x_{2} = \frac{11 \pi}{6}$$
Numerical answer
[src]
x1 = 194.255145746969
x2 = 30.8923277602996
x3 = -43.4586983746588
x4 = 5.75958653158129
x5 = 62.3082542961976
x6 = -5.75958653158129
x7 = 100.007366139275
x8 = -18.3259571459405
x9 = 75.9218224617533
x10 = -94.7713783832921
x11 = 38.2227106186758
x12 = -88.4881930761125
x13 = -37.1755130674792
x14 = 44.5058959258554
x15 = 57.0722665402146
x16 = -100.007366139275
x17 = -6.80678408277789
x18 = 6.80678408277789
x19 = 12.0427718387609
x20 = 81.1578102177363
x21 = 63.3554518473942
x22 = -63.3554518473942
x23 = 19.3731546971371
x24 = -62.3082542961976
x25 = -75.9218224617533
x26 = 13.0899693899575
x27 = -81.1578102177363
x28 = 18.3259571459405
x29 = 87.4409955249159
x30 = -38.2227106186758
x31 = 43.4586983746588
x32 = 69.6386371545737
x33 = 1168.1488683598
x34 = -12.0427718387609
x35 = -25.6563400043166
x36 = -101.054563690472
x37 = -13.0899693899575
x38 = -19.3731546971371
x39 = 49.7418836818384
x40 = 88.4881930761125
x41 = 24.60914245312
x42 = 68.5914396033772
x43 = 74.8746249105567
x44 = -57.0722665402146
x45 = 56.025068989018
x46 = -30.8923277602996
x47 = -74.8746249105567
x48 = -44.5058959258554
x49 = -56.025068989018
x50 = 31.9395253114962
x51 = 50.789081233035
x52 = 82.2050077689329
x53 = -24.60914245312
x54 = -31.9395253114962
x55 = 37.1755130674792
x56 = 93.7241808320955
x57 = -87.4409955249159
x58 = -93.7241808320955
x59 = -0.523598775598299
x60 = -50.789081233035
x61 = 0.523598775598299
x62 = 25.6563400043166
x63 = -82.2050077689329
x64 = -49.7418836818384
x65 = -69.6386371545737
x66 = 94.7713783832921
x67 = -68.5914396033772
x67 = -68.5914396033772
The graph