Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+6x-7=0
-
Equation x*x-x+7=0
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Equation 5*sqrt(x-3)=-2
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Equation x^2-14*x+33=0
- Express {x} in terms of y where:
- 1*x+18*y=-5
- -9*x+12*y=16
- -9*x+1*y=20
- -3*x+16*y=20
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)=-(two / five)
- co sinus of e of (x) equally minus (2 divide by 5)
- co sinus of e of (x) equally minus (two divide by five)
- cosx=-2/5
- cos(x)=-(2 divide by 5)
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Similar expressions
- cos(x/3+pi/4)=1/2
- 3/10=-2/5*a
- 5-2/5*x=11
- ((2x+1)/3)-((7x+5)/15)=((x-2)/5)+(2/3)
- x+3/6=3x-2/5
- cos(x)=+(2/5)
- cosx=-(2/5)
cos(x)=-(2/5) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{2}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{2}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(-2/5) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(- \frac{2}{5} \right)} + 2 \pi$$
x2 = acos(-2/5)
$$x_{2} = \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
x2 = acos(-2/5)
Sum and product of roots
[src]
sum
-acos(-2/5) + 2*pi + acos(-2/5)
$$\operatorname{acos}{\left(- \frac{2}{5} \right)} + \left(- \operatorname{acos}{\left(- \frac{2}{5} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(-2/5) + 2*pi)*acos(-2/5)
$$\left(- \operatorname{acos}{\left(- \frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
=
(-acos(-2/5) + 2*pi)*acos(-2/5)
$$\left(- \operatorname{acos}{\left(- \frac{2}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{2}{5} \right)}$$
(-acos(-2/5) + 2*pi)*acos(-2/5)
Numerical answer
[src]
x1 = 48.2831692845743
x2 = -96.2300927805562
x3 = -39.6814250159399
x4 = 67.1327252061131
x5 = -1.98231317286238
x6 = -58.5309809374787
x7 = -54.5663545917539
x8 = -79.6990958204722
x9 = 98.548651742011
x10 = -45.9646103231195
x11 = -16.8672427486764
x12 = 23.150428055856
x13 = -5822.53046658261
x14 = 85.9822811276518
x15 = 20.8318690944011
x16 = 39.6814250159399
x17 = 71.0973515518378
x18 = 16.8672427486764
x19 = 35.7167986702151
x20 = -92.2654664348314
x21 = -60.8495398989335
x22 = 4.3008721343172
x23 = 92.2654664348314
x24 = 14.5486837872216
x25 = -4.3008721343172
x26 = 54.5663545917539
x27 = -83.663722166197
x28 = 64.8141662446583
x29 = 89.9469074733766
x30 = -27.1150544015807
x31 = -77.3805368590174
x32 = 58.5309809374787
x33 = -52.2477956302991
x34 = -67.1327252061131
x35 = -85.9822811276518
x36 = -33.3982397087603
x37 = -35.7167986702151
x38 = 33.3982397087603
x39 = 41.9999839773947
x40 = 60.8495398989335
x41 = -64.8141662446583
x42 = -41.9999839773947
x43 = -14.5486837872216
x44 = -73.4159105132927
x45 = 96.2300927805562
x46 = -98.548651742011
x47 = 10.5840574414968
x48 = 27.1150544015807
x49 = -20.8318690944011
x50 = 73.4159105132927
x51 = 29.4336133630355
x52 = -89.9469074733766
x53 = -48.2831692845743
x54 = 45.9646103231195
x55 = 77.3805368590174
x56 = 79.6990958204722
x57 = 83.663722166197
x58 = -8.26549848004197
x59 = -29.4336133630355
x60 = -71.0973515518378
x61 = -23.150428055856
x62 = 8.26549848004197
x63 = -10.5840574414968
x64 = 52.2477956302991
x65 = 1.98231317286238
x65 = 1.98231317286238
The graph