Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-x-7=0
-
Equation x^2+x-9=0
-
Equation -2(-2-y)-y-2=0
-
Equation x+5=13
- Express {x} in terms of y where:
- -6*x-13*y=17
- -7*x+5*y=1
- -6*x-19*y=7
- -19*x-4*y=-19
- Derivative of:
-
sin(4*x)
-
-1
- Graphing y =:
-
sin(4*x)
- Limit of the function:
-
sin(4*x)
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- sin(four *x)=- one
- sinus of (4 multiply by x) equally minus 1
- sinus of (four multiply by x) equally minus one
- sin(4x)=-1
- sin4x=-1
-
Similar expressions
- sin(4*x+p/3)=0
- (sin(4x)(sin(2x))^2+sin(2x)^3)/(5tg(x)+4tg(x)cos(2x))=2
- cos2x-sin4x=0
- sin(4*x)=+1
- sin(4x)-3^(1/2)/2=0
sin(4*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(4 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$4 x = 2 \pi n - \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{3 \pi}{8}$$
$$\sin{\left(4 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$4 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$4 x = 2 \pi n - \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$4$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{3 \pi}{8}$$
Rapid solution
[src]
-pi
x1 = ----
8
$$x_{1} = - \frac{\pi}{8}$$
3*pi
x2 = ----
8
$$x_{2} = \frac{3 \pi}{8}$$
x2 = 3*pi/8
Sum and product of roots
[src]
sum
pi 3*pi - -- + ---- 8 8
$$- \frac{\pi}{8} + \frac{3 \pi}{8}$$
=
pi -- 4
$$\frac{\pi}{4}$$
product
-pi 3*pi ----*---- 8 8
$$- \frac{\pi}{8} \frac{3 \pi}{8}$$
=
2 -3*pi ------ 64
$$- \frac{3 \pi^{2}}{64}$$
-3*pi^2/64
Numerical answer
[src]
x1 = -77.3617191922663
x2 = 42.0188017154946
x3 = -47.5165889944504
x4 = -17.6714587255811
x5 = 20.0276531244896
x6 = -3.53429183982371
x7 = -25.5254404172294
x8 = 5.89048630601688
x9 = -53.7997741489889
x10 = -80.5033119347586
x11 = -58.512163418571
x12 = -31.8086255639604
x13 = -75.7909227331784
x14 = 27.8816348852699
x15 = -82.0741080135087
x16 = -22.3838475557172
x17 = -14.5298663255924
x18 = 98.5674693889903
x19 = -91.498886148304
x20 = -38.0918108532085
x21 = -69.5077375714784
x22 = 84.4303024715116
x23 = 4.31968985434627
x24 = 62.4391538934323
x25 = 90.7134878811712
x26 = 18.4568567377593
x27 = -33.3794220507366
x28 = -61.6537558849751
x29 = 48.301987014692
x30 = -88.3572932691129
x31 = 78.1471173828293
x32 = -8.24668059419322
x33 = -9.81747697788046
x34 = -97.7820713166882
x35 = -39.6626073053534
x36 = -11.3882734788215
x37 = -44.374996126151
x38 = -16.1006622734711
x39 = -52.2289777470169
x40 = 70.2931355951281
x41 = 79.7179137087287
x42 = 13.7444679818906
x43 = 76.5763208145247
x44 = -30.237829170498
x45 = -96.2112749006757
x46 = 10.6028750937315
x47 = 68.7223393336083
x48 = 93.8550806217218
x49 = 92.2842841757553
x50 = 40.4480053155132
x51 = 27.8816346273068
x52 = -85.215700617134
x53 = 43.5895981498367
x54 = -60.0829594332135
x55 = 24.7400422576775
x56 = 64.0099503040047
x57 = 12.1736716095332
x58 = 21.5984495824462
x59 = -83.6449044644497
x60 = 2.74889373159412
x61 = -89.9280899395631
x62 = -41.233403301565
x63 = -66.3661446973152
x64 = 56.1559687898059
x65 = 84.4303027206186
x66 = 86.0010988906895
x67 = 57.7267651333619
x68 = -23.9546440698867
x69 = -36.5210148980811
x70 = 26.3108384344347
x71 = 46.7311907920314
x72 = -67.9369412996327
x73 = 100.138265970845
x74 = 34.1648201986395
x75 = 49.8727834642995
x76 = 48.3019869823087
x77 = 32.594023666847
x78 = -45.9457926779855
x79 = 35.7356165577455
x80 = -0.392698986134672
x81 = -74.2201263237444
x82 = 71.8639320431144
x83 = -63.2245518402327
x84 = -19.2422547864247
x85 = -367.959039667966
x86 = 87.5718952800362
x87 = 65.5807467157997
x88 = -1.96349547006081
x89 = -55.370570621922
x90 = 54.5851722404622
x91 = -99.3528677616324
x91 = -99.3528677616324
The graph