Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^3=27
-
Equation x^4+2*x^2-8=0
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Equation cos(x)=2/3
-
Equation (x-11)^4=(x+3)^4
- Express {x} in terms of y where:
- 6*x+17*y=3
- 1*x+4*y=20
- 20*x+7*y=-9
- -17*x+18*y=10
- Derivative of:
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cos(x)
- 2/3
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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2/3
- Canonical form:
- 2/3
-
Identical expressions
- cos(x)= two / three
- co sinus of e of (x) equally 2 divide by 3
- co sinus of e of (x) equally two divide by three
- cosx=2/3
- cos(x)=2 divide by 3
-
Similar expressions
- (x-2)/3=y+1/4=z-3/2
- (x-5)2=2*(3x/7-1/2)/3
- cos(x^2)=0
- cosx=-√2/2
- cosx=2/3
cos(x)=2/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{2}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{2}{3} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-acos(2/3) + 2*pi + acos(2/3)
$$\operatorname{acos}{\left(\frac{2}{3} \right)} + \left(- \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(2/3) + 2*pi)*acos(2/3)
$$\left(- \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{3} \right)}$$
=
(-acos(2/3) + 2*pi)*acos(2/3)
$$\left(- \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{3} \right)}$$
(-acos(2/3) + 2*pi)*acos(2/3)
Rapid solution
[src]
x1 = -acos(2/3) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi$$
x2 = acos(2/3)
$$x_{2} = \operatorname{acos}{\left(\frac{2}{3} \right)}$$
x2 = acos(2/3)
Numerical answer
[src]
x1 = -19.6906245921067
x2 = 43.1412284796892
x3 = -74.5571550155871
x4 = -36.8580431725096
x5 = 5.44211663661166
x6 = -5.44211663661166
x7 = 51.1065511280046
x8 = 88.8056629710821
x9 = 25.9738098992863
x10 = -63.6729217423638
x11 = -76.239292356723
x12 = 32.2569952064659
x13 = -101.372033585441
x14 = -49.4244137868688
x15 = 24.2916725581504
x16 = -13.4074392849271
x17 = -57.3897364351842
x18 = 63.6729217423638
x19 = 87.1235256299463
x20 = -44.823365820825
x21 = 68.2739697084075
x22 = -25.9738098992863
x23 = 44.823365820825
x24 = -68.2739697084075
x25 = 13.4074392849271
x26 = 61.9907844012279
x27 = -82.5224776639025
x28 = -88.8056629710821
x29 = 7.12425397774752
x30 = -87.1235256299463
x31 = -69.9561070495434
x32 = 76.239292356723
x33 = 38.5401805136454
x34 = -80.8403403227667
x35 = -43.1412284796892
x36 = 49.4244137868688
x37 = 18.0084872509708
x38 = 95.0888482782617
x39 = -30.57485786533
x40 = 69.9561070495434
x41 = 30.57485786533
x42 = 74.5571550155871
x43 = -55.7075990940483
x44 = 0.84106867056793
x45 = -61.9907844012279
x46 = -0.84106867056793
x47 = -18.0084872509708
x48 = 55.7075990940483
x49 = 82.5224776639025
x50 = 57.3897364351842
x51 = 80.8403403227667
x52 = 19.6906245921067
x53 = -93.4067109371259
x54 = -95.0888482782617
x55 = -51.1065511280046
x56 = -11.7253019437912
x57 = -99.6898962443055
x58 = -32.2569952064659
x59 = -7.12425397774752
x60 = 11.7253019437912
x61 = -38.5401805136454
x62 = 36.8580431725096
x63 = 93.4067109371259
x64 = 99.6898962443055
x65 = -24.2916725581504
x65 = -24.2916725581504
The graph