Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-4)^2-x^2=0
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Equation 1/x^2-3/x-4=0
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Equation 6=8-5(7x-1)
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Equation (-x-4)*(3*x+3)=0
- Express {x} in terms of y where:
- -10*x+15*y=10
- 5*x-14*y=-15
- -13*x-7*y=11
- -18*x-10*y=12
- 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)=- zero , three
- co sinus of e of (x) equally minus 0,3
- co sinus of e of (x) equally minus zero , three
- cosx=-0,3
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Similar expressions
- cosx=-√2/2
- cos(x)=+0,3
- cosx=-0,3
cos(x)=-0,3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{3}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
, where n - is a integer
$$\cos{\left(x \right)} = - \frac{3}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
Or
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
, where n - is a integer
Rapid solution
[src]
x1 = -acos(-3/10) + 2*pi
$$x_{1} = - \operatorname{acos}{\left(- \frac{3}{10} \right)} + 2 \pi$$
x2 = acos(-3/10)
$$x_{2} = \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
x2 = acos(-3/10)
Sum and product of roots
[src]
sum
-acos(-3/10) + 2*pi + acos(-3/10)
$$\operatorname{acos}{\left(- \frac{3}{10} \right)} + \left(- \operatorname{acos}{\left(- \frac{3}{10} \right)} + 2 \pi\right)$$
=
2*pi
$$2 \pi$$
product
(-acos(-3/10) + 2*pi)*acos(-3/10)
$$\left(- \operatorname{acos}{\left(- \frac{3}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
=
(-acos(-3/10) + 2*pi)*acos(-3/10)
$$\left(- \operatorname{acos}{\left(- \frac{3}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{10} \right)}$$
(-acos(-3/10) + 2*pi)*acos(-3/10)
Numerical answer
[src]
x1 = 60.9563640909856
x2 = 1.87548898081029
x3 = 4.40769632636929
x4 = -8.15867428798988
x5 = -48.3899934766264
x6 = 23.2572522479081
x7 = -58.4241567454266
x8 = -77.2737126669653
x9 = -52.140971438247
x10 = -39.5746008238878
x11 = -23.2572522479081
x12 = 45.8577861310674
x13 = -29.5404375550876
x14 = 20.7250449023491
x15 = -45.8577861310674
x16 = 89.8400832813245
x17 = 10.6908816335489
x18 = -10.6908816335489
x19 = 58.4241567454266
x20 = 39.5746008238878
x21 = -142.63777308432
x22 = 14.4418595951695
x23 = -42.1068081694468
x24 = 48.3899934766264
x25 = 54.673178783806
x26 = -67.2395493981652
x27 = 8.15867428798988
x28 = 73.5227347053447
x29 = -16.9740669407285
x30 = 83.5568979741449
x31 = -70.9905273597857
x32 = 29.5404375550876
x33 = 70.9905273597857
x34 = -54.673178783806
x35 = -86.0891053197039
x36 = -33.2914155167082
x37 = 98.6554759340631
x38 = -73.5227347053447
x39 = 92.3722906268835
x40 = 64.7073420526062
x41 = 284.618827803892
x42 = -27.0082302095286
x43 = 33.2914155167082
x44 = -4.40769632636929
x45 = -14.4418595951695
x46 = 96.1232685885041
x47 = -83.5568979741449
x48 = -35.8236228622672
x49 = 79.8059200125243
x50 = -92.3722906268835
x51 = 27.0082302095286
x52 = -1.87548898081029
x53 = -60.9563640909856
x54 = 86.0891053197039
x55 = -98.6554759340631
x56 = -96.1232685885041
x57 = 42.1068081694468
x58 = -79.8059200125243
x59 = 35.8236228622672
x60 = -89.8400832813245
x61 = 52.140971438247
x62 = 16.9740669407285
x63 = 67.2395493981652
x64 = 77.2737126669653
x65 = -64.7073420526062
x66 = -20.7250449023491
x66 = -20.7250449023491
The graph