Mister Exam
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How to use it?
- Equation:
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Equation x*(x^2+8*x+16)=5*(x+4)
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Equation -x^2+4x+3=x^2-x-(1+2x^2)
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Identical expressions
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Similar expressions
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2*cos(x)/2=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{2 \cos{\left(x \right)}}{2} = 0$$
- this is the simplest trigonometric equation
We get:
$$\frac{2 \cos{\left(x \right)}}{2} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x = \pi n + \frac{\pi}{2}$$
$$x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
$$\frac{2 \cos{\left(x \right)}}{2} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\frac{2 \cos{\left(x \right)}}{2} = 0$$
This equation is transformed to
$$x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x = \pi n + \frac{\pi}{2}$$
$$x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Rapid solution
[src]
pi
x1 = --
2
$$x_{1} = \frac{\pi}{2}$$
3*pi
x2 = ----
2
$$x_{2} = \frac{3 \pi}{2}$$
x2 = 3*pi/2
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 2 2
$$\frac{\pi}{2} + \frac{3 \pi}{2}$$
=
2*pi
$$2 \pi$$
product
pi 3*pi --*---- 2 2
$$\frac{\pi}{2} \frac{3 \pi}{2}$$
=
2 3*pi ----- 4
$$\frac{3 \pi^{2}}{4}$$
3*pi^2/4
Numerical answer
[src]
x1 = 7.85398163397448
x2 = -2266.65909956504
x3 = -86.3937979737193
x4 = 58.1194640914112
x5 = 23.5619449019235
x6 = -67.5442420521806
x7 = -4.71238898038469
x8 = -20.4203522483337
x9 = 83.2522053201295
x10 = -29.845130209103
x11 = -39.2699081698724
x12 = -98.9601685880785
x13 = 98.9601685880785
x14 = 86.3937979737193
x15 = 26.7035375555132
x16 = -48.6946861306418
x17 = -89.5353906273091
x18 = -17.2787595947439
x19 = 20.4203522483337
x20 = 48.6946861306418
x21 = -64.4026493985908
x22 = 67.5442420521806
x23 = 14.1371669411541
x24 = -26.7035375555132
x25 = 42.4115008234622
x26 = -70.6858347057703
x27 = -32.9867228626928
x28 = 39.2699081698724
x29 = 4.71238898038469
x30 = 73.8274273593601
x31 = 89.5353906273091
x32 = 45.553093477052
x33 = 70.6858347057703
x34 = -168.075206967054
x35 = -7.85398163397448
x36 = -95.8185759344887
x37 = 76.9690200129499
x38 = 32.9867228626928
x39 = -23.5619449019235
x40 = 64.4026493985908
x41 = -36.1283155162826
x42 = -83.2522053201295
x43 = -1.5707963267949
x44 = -58.1194640914112
x45 = -387.986692718339
x46 = -10.9955742875643
x47 = 1.5707963267949
x48 = 29.845130209103
x49 = -73.8274273593601
x50 = -92.6769832808989
x51 = -54.9778714378214
x52 = 80.1106126665397
x53 = 54.9778714378214
x54 = -76.9690200129499
x55 = 36.1283155162826
x56 = 61.261056745001
x57 = 92.6769832808989
x58 = -61.261056745001
x59 = 17.2787595947439
x60 = 10.9955742875643
x61 = -51.8362787842316
x62 = -45.553093477052
x63 = -42.4115008234622
x64 = -80.1106126665397
x65 = 51.8362787842316
x66 = 95.8185759344887
x67 = -14.1371669411541
x67 = -14.1371669411541