Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)=1
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Equation cos(x)=1/3
-
Equation k^2-4*k+13=0
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Equation k^2-4*k+3=0
- Express {x} in terms of y where:
- -14*x+1*y=3
- -11*x+4*y=-8
- 16*x+7*y=8
- 17*x-11*y=2
- Derivative of:
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cos(x)
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1/3
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
- Sum of series:
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1/3
- Limit of the function:
- 1/3
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Identical expressions
- cos(x)= one / three
- co sinus of e of (x) equally 1 divide by 3
- co sinus of e of (x) equally one divide by three
- cosx=1/3
- cos(x)=1 divide by 3
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Similar expressions
- 2sin^2x+3sinxcosx-5cos^2x=0
- ((25cos^2x)+24cosx)/(24tgx−7)=0
- cos(pi*(x-1)/3)=1/2
- sin2xcosx-sinxcos2x=1
- cosx=1/3
cos(x)=1/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{3} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(1/3) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi$$
x2 = acos(1/3)
$$x_{2} = \operatorname{acos}{\left(\frac{1}{3} \right)}$$
x2 = acos(1/3)
Sum and product of roots
[src]
sum
-acos(1/3) + 2*pi + acos(1/3)
$$\operatorname{acos}{\left(\frac{1}{3} \right)} + \left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(1/3) + 2*pi)*acos(1/3)
$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$
=
(-acos(1/3) + 2*pi)*acos(1/3)
$$\left(- \operatorname{acos}{\left(\frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{3} \right)}$$
(-acos(1/3) + 2*pi)*acos(1/3)
Numerical answer
[src]
x1 = -5.05222588983881
x2 = -89.195553717855
x3 = 49.0345230400959
x4 = -86.7336348831734
x5 = -1.23095941734077
x6 = -51.4964418747775
x7 = -13.7973300316999
x8 = -45.2132565675979
x9 = -7.51414472452036
x10 = 17.618596504198
x11 = 42.7513377329163
x12 = -55.3177083472755
x13 = 38.9300712604183
x14 = 93.016820190353
x15 = 76.6291831034958
x16 = -76.6291831034958
x17 = 95.4787390250346
x18 = -95.4787390250346
x19 = -23.9017818113776
x20 = 5.05222588983881
x21 = -67.8840789616347
x22 = -32.6468859532387
x23 = 51.4964418747775
x24 = -82.9123684106754
x25 = 82.9123684106754
x26 = 89.195553717855
x27 = 61.6008936544551
x28 = -26.3637006460591
x29 = -64.0628124891366
x30 = 55.3177083472755
x31 = -93.016820190353
x32 = -101.761924332214
x33 = -74.1672642688143
x34 = -325.494676555998
x35 = 23.9017818113776
x36 = 32.6468859532387
x37 = -61.6008936544551
x38 = 7.51414472452036
x39 = 64.0628124891366
x40 = 30.1849671185572
x41 = 11.3354111970184
x42 = 99.3000054975326
x43 = -11.3354111970184
x44 = 74.1672642688143
x45 = -17.618596504198
x46 = 57.7796271819571
x47 = 13.7973300316999
x48 = -70.3459977963162
x49 = 26.3637006460591
x50 = -30.1849671185572
x51 = 36.4681524257367
x52 = 45.2132565675979
x53 = -49.0345230400959
x54 = 67.8840789616347
x55 = -20.0805153388795
x56 = -99.3000054975326
x57 = -36.4681524257367
x58 = 20.0805153388795
x59 = -57.7796271819571
x60 = -80.4504495759938
x61 = 86.7336348831734
x62 = -42.7513377329163
x63 = -38.9300712604183
x64 = 80.4504495759938
x65 = 1.23095941734077
x66 = 70.3459977963162
x66 = 70.3459977963162
The graph