Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-2x-15=0
-
Equation k^2+4=0
- Equation 3x^2-28x+9=0
-
Equation 8-5(8+3x)=13
- Express {x} in terms of y where:
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
- -4*x+18*y=-14
- Derivative of:
-
cos2x
- Integral of d{x}:
-
cos2x
- Graphing y =:
- cos2x
-
Identical expressions
- cos2x
- co sinus of e of 2x
-
Similar expressions
- 5-8cos^2x=sin2x
- 16sin^4(x)+8cos2(x)-7=0
- cos(2x)+sin((pi/2)-x)+1=0
- cos^2x-3sinxcosx+2sin^2x=2
cos2x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\cos{\left(2 x \right)} = 0$$
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:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4}$$
$$\cos{\left(2 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\cos{\left(2 x \right)} = 0$$
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 = 18.0641577581413
x2 = -46.3384916404494
x3 = 52.621676947629
x4 = 49.4800842940392
x5 = 33.7721210260903
x6 = 38.484510006475
x7 = -2.35619449019234
x8 = -69.9004365423729
x9 = 32.2013246992954
x10 = 46.3384916404494
x11 = 60.4756585816035
x12 = -98.174770424681
x13 = -82.4668071567321
x14 = 30.6305283725005
x15 = -91.8915851175014
x16 = 47.9092879672443
x17 = 162.577419823272
x18 = 54.1924732744239
x19 = 19.6349540849362
x20 = 11.7809724509617
x21 = 69.9004365423729
x22 = -19.6349540849362
x23 = 1973.70558461779
x24 = 68.329640215578
x25 = 384.059701901352
x26 = -57.3340659280137
x27 = -24.3473430653209
x28 = -85.6083998103219
x29 = -47.9092879672443
x30 = 16.4933614313464
x31 = -32.2013246992954
x32 = 25.9181393921158
x33 = 40.0553063332699
x34 = -33.7721210260903
x35 = 44.7676953136546
x36 = -12461.9126586273
x37 = 8.63937979737193
x38 = 27.4889357189107
x39 = -79.3252145031423
x40 = 24.3473430653209
x41 = -25.9181393921158
x42 = 22.776546738526
x43 = -13.3517687777566
x44 = -16.4933614313464
x45 = -62.0464549083984
x46 = -49.4800842940392
x47 = -5.49778714378214
x48 = 87.1791961371168
x49 = 10.2101761241668
x50 = 76.1836218495525
x51 = 99.7455667514759
x52 = 90.3207887907066
x53 = -35.3429173528852
x54 = -3.92699081698724
x55 = -55.7632696012188
x56 = -93.4623814442964
x57 = -40.0553063332699
x58 = -68.329640215578
x59 = 77.7544181763474
x60 = 91.8915851175014
x61 = -99.7455667514759
x62 = 66.7588438887831
x63 = -38.484510006475
x64 = 55.7632696012188
x65 = -41.6261026600648
x66 = -54.1924732744239
x67 = 2.35619449019234
x68 = -90.3207887907066
x69 = -76.1836218495525
x70 = -77.7544181763474
x71 = 3.92699081698724
x72 = 5.49778714378214
x73 = -18.0641577581413
x74 = -84.037603483527
x75 = -11.7809724509617
x76 = 88.7499924639117
x77 = 74.6128255227576
x78 = -10.2101761241668
x79 = -71.4712328691678
x80 = -27.4889357189107
x81 = 82.4668071567321
x82 = 63.6172512351933
x83 = 62.0464549083984
x84 = 85.6083998103219
x85 = 41.6261026600648
x86 = 98.174770424681
x87 = 96.6039740978861
x88 = -63.6172512351933
x89 = 84.037603483527
x90 = -60.4756585816035
x90 = -60.4756585816035