Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin2x=-1
-
Equation sqrt(x-1)=3-x
-
Equation sin3x=1
-
Equation cot(x)=1
- Express {x} in terms of y where:
- 12*x+14*y=-15
- 4*x-7*y=4
- -6*x-12*y=9
- -10*x-18*y=6
- Graphing y =:
-
sin2x
- Derivative of:
-
sin2x
-
-1
- Sum of series:
- sin2x
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- sin2x=- one
- sinus of 2x equally minus 1
- sinus of 2x equally minus one
-
Similar expressions
- sin(x)+sin(2*x)+sin(3*x)=0
- sin(x-(1/2))-x+(1/2)=0
- sin(4x)+sin(3x)+sin(2x)=0
- sin2x=+1
sin2x=-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
$$x_{2} = \frac{3 \pi}{4}$$
x2 = 3*pi/4
Sum and product of roots
[src]
sum
pi 3*pi - -- + ---- 4 4
$$- \frac{\pi}{4} + \frac{3 \pi}{4}$$
=
pi -- 2
$$\frac{\pi}{2}$$
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
Numerical answer
[src]
x1 = -73.0420291965934
x2 = 87.1791959595656
x3 = -54.1924731445711
x4 = 43.1968988259316
x5 = -91.8915845717239
x6 = -0.785397916651749
x7 = 2.35619442440536
x8 = 84.0376034199549
x9 = -60.4756583509459
x10 = 11.7809725930891
x11 = 40.0553062099627
x12 = -16.4933611966261
x13 = -88.7499922112266
x14 = -76.1836217239439
x15 = 46.3384915843947
x16 = 58.9048620066655
x17 = -88.7499925537801
x18 = 68.3296401645238
x19 = -66.7588439932285
x20 = -44.7676950635734
x21 = 90.3207887447523
x22 = -60.4756585174615
x23 = -19.6349541554673
x24 = 30.6305281863893
x25 = -85.608399894653
x26 = -98.1747703033985
x27 = 5.49778738042301
x28 = -29.0597322955756
x29 = -22.7765468685351
x30 = -51.0508808708243
x31 = -0.785398304611266
x32 = 71.471233111112
x33 = 21.2057506565108
x34 = -95.0331780209134
x35 = -63.6172513149926
x36 = -38.4845103583538
x37 = 36.9137135281996
x38 = -13.3517689698773
x39 = 8.63937960822746
x40 = -10.2101759860574
x41 = 96.6039739212089
x42 = -82.4668069282144
x43 = -7.06858355298869
x44 = -41.6261027352652
x45 = 14.9225649892472
x46 = -35.3429175479242
x47 = 24.3473430043575
x48 = -35.3429178934093
x49 = 49.4800845342934
x50 = -38.4845097737495
x51 = -3.92699107594367
x52 = 62.0464547256144
x53 = 36.9137134309271
x54 = -44.7676954314418
x55 = 18.0641575837788
x56 = 55.7632697006301
x57 = -32.2013245652766
x58 = 87.1791963746667
x59 = -7.0685837201977
x60 = 80.896010582516
x61 = 93.462381687851
x62 = 74.6128253428807
x63 = 33.7721211721652
x64 = -22.7765464900166
x65 = 80.8960105951638
x66 = 55.7632697511726
x67 = 14.9225648553046
x68 = -73.0420294459387
x69 = 27.4889359573966
x70 = 99.7455669089878
x71 = 52.6216767646073
x72 = -29.0597320982225
x73 = 62.0464548195549
x74 = 43.1968992294597
x75 = -79.3252147038408
x76 = 58.9048620635881
x77 = 77.7544183301131
x78 = -101.316363786262
x79 = -96953.4762811305
x80 = -51.0508806461775
x81 = -76.1836225361187
x82 = 21.2057502602382
x83 = 65.1880473923958
x84 = 65.1880478021829
x85 = -57.3340661259123
x86 = -95.0331777492301
x87 = 96.6039739773235
x88 = -66.758843637313
x88 = -66.758843637313
The graph