Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x^2-8*x-3=0
-
Equation (x+2)*4+28=(x-2)*2
-
Equation cos(3*x)=0
-
Equation -2x=24
- Express {x} in terms of y where:
- 11*x-6*y=-1
- -17*x-11*y=16
- -11*x+13*y=10
- 15*x+2*y=8
- Graphing y =:
- cos(3*x)
- Derivative of:
-
cos(3*x)
- Integral of d{x}:
-
cos(3*x)
-
Identical expressions
- cos(three *x)= zero
- co sinus of e of (3 multiply by x) equally 0
- co sinus of e of (three multiply by x) equally zero
- cos(3x)=0
- cos3x=0
- cos(3*x)=O
-
Similar expressions
- 2cos^3(x)-2sin^2(x)=-1
- since+sin3x+cost+cos3x=0
- sinx-cos3x+cosx=0
cos(3*x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$3 x = \pi n + \frac{\pi}{2}$$
$$3 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{6}$$
$$\cos{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$3 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$3 x = \pi n + \frac{\pi}{2}$$
$$3 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{3} - \frac{\pi}{6}$$
Rapid solution
[src]
pi
x1 = --
6
$$x_{1} = \frac{\pi}{6}$$
pi
x2 = --
2
$$x_{2} = \frac{\pi}{2}$$
x2 = pi/2
Sum and product of roots
[src]
sum
pi pi -- + -- 6 2
$$\frac{\pi}{6} + \frac{\pi}{2}$$
=
2*pi ---- 3
$$\frac{2 \pi}{3}$$
product
pi pi --*-- 6 2
$$\frac{\pi}{6} \frac{\pi}{2}$$
=
2 pi --- 12
$$\frac{\pi^{2}}{12}$$
pi^2/12
Numerical answer
[src]
x1 = 88.4881930761125
x2 = -56.025068989018
x3 = -47.6474885794452
x4 = 64.4026493985908
x5 = 20.4203522483337
x6 = -34.0339204138894
x7 = 62.3082542961976
x8 = -58.1194640914112
x9 = 38.2227106186758
x10 = 75.9218224617533
x11 = 78.0162175641465
x12 = -80.1106126665397
x13 = 84.2994028713261
x14 = 49.7418836818384
x15 = 18.3259571459405
x16 = -69.6386371545737
x17 = 80.1106126665397
x18 = -75.9218224617533
x19 = -7.85398163397448
x20 = 100.007366139275
x21 = 44.5058959258554
x22 = 71.733032256967
x23 = -45.553093477052
x24 = -21.4675497995303
x25 = -49.7418836818384
x26 = 93.7241808320955
x27 = 86.3937979737193
x28 = -38.2227106186758
x29 = 15.1843644923507
x30 = -100.007366139275
x31 = -89.5353906273091
x32 = -25.6563400043166
x33 = 26.7035375555132
x34 = -16.2315620435473
x35 = 34.0339204138894
x36 = -1.5707963267949
x37 = 9.94837673636768
x38 = -95.8185759344887
x39 = 36.1283155162826
x40 = 41.3643032722656
x41 = 58.1194640914112
x42 = 16.2315620435473
x43 = 12.0427718387609
x44 = -82.2050077689329
x45 = -27.7507351067098
x46 = 5.75958653158129
x47 = -60.2138591938044
x48 = 7.85398163397448
x49 = 73.8274273593601
x50 = 66.497044500984
x51 = -84.2994028713261
x52 = 95.8185759344887
x53 = 22.5147473507269
x54 = -36.1283155162826
x55 = -97.9129710368819
x56 = -23.5619449019235
x57 = 1676.03968069015
x58 = -43.4586983746588
x59 = -61.261056745001
x60 = 1.5707963267949
x61 = -62.3082542961976
x62 = 56.025068989018
x63 = -51.8362787842316
x64 = -29.845130209103
x65 = -78.0162175641465
x66 = -93.7241808320955
x67 = -73.8274273593601
x68 = 68.5914396033772
x69 = 40.317105721069
x70 = -91.6297857297023
x71 = 91.6297857297023
x72 = -98.9601685880785
x73 = 27.7507351067098
x74 = -5.75958653158129
x75 = 29.845130209103
x76 = -65.4498469497874
x77 = 87.4409955249159
x78 = -9.94837673636768
x79 = 42.4115008234622
x80 = -19.3731546971371
x81 = -71.733032256967
x82 = -53.9306738866248
x83 = -12.0427718387609
x84 = 82.2050077689329
x85 = 97.9129710368819
x86 = -14.1371669411541
x87 = 31.9395253114962
x88 = -31.9395253114962
x89 = 0.523598775598299
x90 = 51.8362787842316
x91 = 53.9306738866248
x92 = -3.66519142918809
x93 = 4.71238898038469
x94 = 60.2138591938044
x95 = 14.1371669411541
x96 = -67.5442420521806
x96 = -67.5442420521806
The graph