Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation log(4/(7-x))/log(x^2)=5
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Equation 2x-5=7
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Equation x^4=(x-20)^2
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Equation sin(x)=1/4
- Express {x} in terms of y where:
- -11*x+6*y=4
- 14*x-13*y=-10
- -14*x-16*y=14
- 16*x-17*y=-9
- Derivative of:
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cos(x)
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-1/3
- Integral of d{x}:
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cos(x)
- Graphing y =:
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cos(x)
- Limit of the function:
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-1/3
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Identical expressions
- cos(x)=- one / three
- co sinus of e of (x) equally minus 1 divide by 3
- co sinus of e of (x) equally minus one divide by three
- cosx=-1/3
- cos(x)=-1 divide by 3
-
Similar expressions
- cosx/5=-(√3/2)
- sinx=cosx
- x-(1/3*x+2)-(1/4*x+1)-((x-(1/3*x+1/4*x+2+1))*0,5)=1/6
- (x-1)/(2x+3)-(2x-1)/(3-2x)=0
- ((2x+1)^2)/25-(x-1)/3=x
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=0
- cos(x)=+1/3
- 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)
$$x_{2} = \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
Sum and product of roots
[src]
sum
0 + -acos(-1/3) + 2*pi + acos(-1/3)
$$\operatorname{acos}{\left(- \frac{1}{3} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi\right)\right)$$
=
2*pi
$$2 \pi$$
product
1*(-acos(-1/3) + 2*pi)*acos(-1/3)
$$1 \left(- \operatorname{acos}{\left(- \frac{1}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{3} \right)}$$
=
(-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 = 52.1761156936857
x2 = 67.2044051427264
x3 = 92.3371463714448
x4 = -14.4770038506082
x5 = -67.2044051427264
x6 = -64.7424863080449
x7 = 83.5920422295836
x8 = -42.0716639140081
x9 = 71.0256716152245
x10 = -77.3088569224041
x11 = 3328.17757956893
x12 = 29.5052932996489
x13 = 1.91063323624902
x14 = 14.4770038506082
x15 = -98.6203316786244
x16 = -8.19381854342861
x17 = 45.8929303865061
x18 = 8.19381854342861
x19 = -45.8929303865061
x20 = -89.8752275367632
x21 = -86.0539610642652
x22 = 64.7424863080449
x23 = -10.6557373781102
x24 = 16.9389226852897
x25 = -27.0433744649674
x26 = -96.1584128439428
x27 = 42.0716639140081
x28 = 58.4593010008653
x29 = 96.1584128439428
x30 = 77.3088569224041
x31 = 35.7884786068285
x32 = 54.6380345283673
x33 = 73.487590449906
x34 = 4.37255207093057
x35 = 48.3548492211877
x36 = 86.0539610642652
x37 = -60.9212198355468
x38 = -971.983089376587
x39 = 60.9212198355468
x40 = -83.5920422295836
x41 = 155.168999443241
x42 = 89.8752275367632
x43 = 10.6557373781102
x44 = -71.0256716152245
x45 = -48.3548492211877
x46 = 39.6097450793265
x47 = -52.1761156936857
x48 = -20.7601891577878
x49 = -35.7884786068285
x50 = -39.6097450793265
x51 = -4.37255207093057
x52 = 79.7707757570856
x53 = -23.2221079924693
x54 = -58.4593010008653
x55 = 20.7601891577878
x56 = 33.326559772147
x57 = -16.9389226852897
x58 = -33.326559772147
x59 = -29.5052932996489
x60 = -92.3371463714448
x61 = -79.7707757570856
x62 = 27.0433744649674
x63 = -54.6380345283673
x64 = 98.6203316786244
x65 = -73.487590449906
x66 = 23.2221079924693
x67 = -1.91063323624902
x67 = -1.91063323624902
The graph