Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=27
-
Equation x^4+2*x^2-8=0
-
Equation cos(x)=2/3
-
Equation (x-11)^4=(x+3)^4
- Express {x} in terms of y where:
- 6*x+17*y=3
- 1*x+4*y=20
- 20*x+7*y=-9
- -17*x+18*y=10
- Derivative of:
-
4cos2x
- Integral of d{x}:
-
4cos2x
-
Identical expressions
- 4cos2x
- 4 co sinus of e of 2x
-
Similar expressions
- 4cos^2x+4sinx+1=0
- 4*cos(2*x)*cos(3*x)+3=6*sin(2*x+3*pi/2)+2*(-cos(3*x))
- 5sinxcosx+14cos^2x=0
- 4cos^2x=3cos2x+1
4cos2x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$4 \cos{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$4 \cos{\left(2 x \right)} = 0$$
The equation is transformed to
$$\cos{\left(2 x \right)} = 0$$
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{2}$$
$$2 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}$$
$$4 \cos{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$4 \cos{\left(2 x \right)} = 0$$
Divide both parts of the equation by 4
The equation is transformed to
$$\cos{\left(2 x \right)} = 0$$
This equation is transformed to
$$2 x = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{2}$$
$$2 x = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}$$
Sum and product of roots
[src]
sum
pi 3*pi -- + ---- 4 4
$$\frac{\pi}{4} + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
product
pi 3*pi --*---- 4 4
$$\frac{\pi}{4} \frac{3 \pi}{4}$$
=
2 3*pi ----- 16
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Rapid solution
[src]
pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
3*pi
x2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
x2 = 3*pi/4
Numerical answer
[src]
x1 = 2.35619449019234
x2 = -11.7809724509617
x3 = -38.484510006475
x4 = 11.7809724509617
x5 = 46.3384916404494
x6 = 40.0553063332699
x7 = -68.329640215578
x8 = -32.2013246992954
x9 = -25.9181393921158
x10 = 33.7721210260903
x11 = 96.6039740978861
x12 = 55.7632696012188
x13 = 384.059701901352
x14 = 5.49778714378214
x15 = -18.0641577581413
x16 = -69.9004365423729
x17 = 18.0641577581413
x18 = -85.6083998103219
x19 = 47.9092879672443
x20 = 76.1836218495525
x21 = 44.7676953136546
x22 = -62.0464549083984
x23 = 32.2013246992954
x24 = 62.0464549083984
x25 = -33.7721210260903
x26 = 88.7499924639117
x27 = 52.621676947629
x28 = -63.6172512351933
x29 = -16.4933614313464
x30 = -10.2101761241668
x31 = -24.3473430653209
x32 = -47.9092879672443
x33 = -12461.9126586273
x34 = 85.6083998103219
x35 = 10.2101761241668
x36 = 41.6261026600648
x37 = 99.7455667514759
x38 = -5.49778714378214
x39 = 24.3473430653209
x40 = -82.4668071567321
x41 = -76.1836218495525
x42 = 22.776546738526
x43 = -60.4756585816035
x44 = -93.4623814442964
x45 = -57.3340659280137
x46 = 82.4668071567321
x47 = 98.174770424681
x48 = 8.63937979737193
x49 = -54.1924732744239
x50 = -35.3429173528852
x51 = -98.174770424681
x52 = 38.484510006475
x53 = 162.577419823272
x54 = -49.4800842940392
x55 = 49.4800842940392
x56 = -27.4889357189107
x57 = 27.4889357189107
x58 = 1973.70558461779
x59 = -84.037603483527
x60 = 19.6349540849362
x61 = -41.6261026600648
x62 = -91.8915851175014
x63 = 77.7544181763474
x64 = 60.4756585816035
x65 = 25.9181393921158
x66 = -90.3207887907066
x67 = -55.7632696012188
x68 = -19.6349540849362
x69 = -13.3517687777566
x70 = 66.7588438887831
x71 = 91.8915851175014
x72 = -3.92699081698724
x73 = -77.7544181763474
x74 = 63.6172512351933
x75 = -79.3252145031423
x76 = 90.3207887907066
x77 = -40.0553063332699
x78 = 30.6305283725005
x79 = 3.92699081698724
x80 = 69.9004365423729
x81 = 54.1924732744239
x82 = 87.1791961371168
x83 = -46.3384916404494
x84 = 84.037603483527
x85 = 68.329640215578
x86 = 74.6128255227576
x87 = -71.4712328691678
x88 = -2.35619449019234
x89 = -99.7455667514759
x90 = 16.4933614313464
x90 = 16.4933614313464