Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x+5+(x+5)=(1-x)+4
-
Equation x-x/7=15/7
-
Equation (cos(pi*x)/(x-2))=1/(x-2)
-
Equation sin(2*x)=-1
- Express {x} in terms of y where:
- 10*x+5*y=-17
- 18*x-14*y=-12
- 20*x+5*y=-3
- -2*x-14*y=7
- Derivative of:
-
sin(2*x)
-
-1
- Integral of d{x}:
-
sin(2*x)
-
-1
- Graphing y =:
- sin(2*x)
- Sum of series:
-
-1
-
Identical expressions
- sin(two *x)=- one
- sinus of (2 multiply by x) equally minus 1
- sinus of (two multiply by x) equally minus one
- sin(2x)=-1
- sin2x=-1
-
Similar expressions
- 3sin(x)^2-3cos(x)-6sin(x)+2sin(2x)+3=0
- 2sin2x+3sinxcosx+5cos2x=0
- sin(2*x)=+1
- 2sin2x–√2·cosx=√2·sinx
- -sin^2x-cos^2x-2sinx=0
sin(2*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(2 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{2}$$
$$2 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{2} = \pi n + \frac{3 \pi}{4}$$
$$\sin{\left(2 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{2}$$
$$2 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n - \frac{\pi}{4}$$
$$x_{2} = \pi n + \frac{3 \pi}{4}$$
Rapid solution
[src]
-pi
x1 = ----
4
$$x_{1} = - \frac{\pi}{4}$$
3*pi
x2 = ----
4
$$x_{2} = \frac{3 \pi}{4}$$
Sum and product of roots
[src]
sum
pi 3*pi
0 - -- + ----
4 4
$$\left(- \frac{\pi}{4} + 0\right) + \frac{3 \pi}{4}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
-pi 3*pi 1*----*---- 4 4
$$\frac{3 \pi}{4} \cdot 1 \left(- \frac{\pi}{4}\right)$$
=
2 -3*pi ------ 16
$$- \frac{3 \pi^{2}}{16}$$
-3*pi^2/16
Numerical answer
[src]
x1 = -35.3429178934093
x2 = -60.4756583509459
x3 = -22.7765464900166
x4 = 90.3207887447523
x5 = -10.2101759860574
x6 = 36.9137135281996
x7 = 58.9048620635881
x8 = -38.4845097737495
x9 = 11.7809725930891
x10 = -13.3517689698773
x11 = -22.7765468685351
x12 = 21.2057502602382
x13 = -76.1836225361187
x14 = -29.0597320982225
x15 = 68.3296401645238
x16 = 30.6305281863893
x17 = -32.2013245652766
x18 = -19.6349541554673
x19 = 52.6216767646073
x20 = -44.7676954314418
x21 = 87.1791959595656
x22 = -60.4756585174615
x23 = 8.63937960822746
x24 = -73.0420291965934
x25 = 93.462381687851
x26 = 49.4800845342934
x27 = 21.2057506565108
x28 = -88.7499925537801
x29 = 33.7721211721652
x30 = -95.0331780209134
x31 = -16.4933611966261
x32 = 84.0376034199549
x33 = -29.0597322955756
x34 = 55.7632697511726
x35 = -54.1924731445711
x36 = -73.0420294459387
x37 = -79.3252147038408
x38 = 80.896010582516
x39 = -41.6261027352652
x40 = 65.1880478021829
x41 = 2.35619442440536
x42 = -88.7499922112266
x43 = -44.7676950635734
x44 = -35.3429175479242
x45 = 43.1968992294597
x46 = -82.4668069282144
x47 = -7.0685837201977
x48 = -101.316363786262
x49 = 87.1791963746667
x50 = -7.06858355298869
x51 = -51.0508808708243
x52 = -76.1836217239439
x53 = 18.0641575837788
x54 = -38.4845103583538
x55 = 14.9225648553046
x56 = -95.0331777492301
x57 = 96.6039739212089
x58 = -96953.4762811305
x59 = 14.9225649892472
x60 = -0.785398304611266
x61 = 99.7455669089878
x62 = 40.0553062099627
x63 = 71.471233111112
x64 = -85.608399894653
x65 = 62.0464547256144
x66 = -91.8915845717239
x67 = -63.6172513149926
x68 = 62.0464548195549
x69 = 77.7544183301131
x70 = 74.6128253428807
x71 = -66.7588439932285
x72 = 80.8960105951638
x73 = -51.0508806461775
x74 = -0.785397916651749
x75 = 43.1968988259316
x76 = 24.3473430043575
x77 = 58.9048620066655
x78 = 96.6039739773235
x79 = 55.7632697006301
x80 = -98.1747703033985
x81 = -66.758843637313
x82 = -3.92699107594367
x83 = 46.3384915843947
x84 = 65.1880473923958
x85 = 5.49778738042301
x86 = -57.3340661259123
x87 = 36.9137134309271
x88 = 27.4889359573966
x88 = 27.4889359573966
The graph