Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 13/(x+6)=2
-
Equation x^2=18
-
Equation -3(x-1)=24-10x
- Equation 7*x^3-63*x=0
- Express {x} in terms of y where:
- 14*x+5*y=11
- 8*x-7*y=-1
- 20*x-5*y=-7
- 3*x-9*y=-4
- Canonical form:
- sin(7*x)
- Derivative of:
-
sin(7*x)
-
-1
- Limit of the function:
-
sin(7*x)
- Sum of series:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- sin(seven *x)=- one
- sinus of (7 multiply by x) equally minus 1
- sinus of (seven multiply by x) equally minus one
- sin(7x)=-1
- sin7x=-1
-
Similar expressions
- sin(7x)-sin(x)=cos(4x)
- sin(7*x)=+1
sin(7*x)=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(7 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$7 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$7 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$7 x = 2 \pi n - \frac{\pi}{2}$$
$$7 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$7$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{7} - \frac{\pi}{14}$$
$$x_{2} = \frac{2 \pi n}{7} + \frac{3 \pi}{14}$$
$$\sin{\left(7 x \right)} = -1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$7 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$7 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Or
$$7 x = 2 \pi n - \frac{\pi}{2}$$
$$7 x = 2 \pi n + \frac{3 \pi}{2}$$
, where n - is a integer
Divide both parts of the equation by
$$7$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{7} - \frac{\pi}{14}$$
$$x_{2} = \frac{2 \pi n}{7} + \frac{3 \pi}{14}$$
Rapid solution
[src]
-pi
x1 = ----
14
$$x_{1} = - \frac{\pi}{14}$$
3*pi
x2 = ----
14
$$x_{2} = \frac{3 \pi}{14}$$
x2 = 3*pi/14
Sum and product of roots
[src]
sum
pi 3*pi - -- + ---- 14 14
$$- \frac{\pi}{14} + \frac{3 \pi}{14}$$
=
pi -- 7
$$\frac{\pi}{7}$$
product
-pi 3*pi ----*---- 14 14
$$- \frac{\pi}{14} \frac{3 \pi}{14}$$
=
2 -3*pi ------ 196
$$- \frac{3 \pi^{2}}{196}$$
-3*pi^2/196
Numerical answer
[src]
x1 = 77.8666179764942
x2 = -73.8274272833876
x3 = -29.8451301122563
x4 = -83.7010043016944
x5 = 30.293929131297
x6 = -47.7970881885378
x7 = -65.7490462508355
x8 = 50.0410829061044
x9 = -5.60998693951112
x10 = -88.1889937368012
x11 = -36.1283154535468
x12 = -80.1106126046346
x13 = -49.592284087747
x14 = 7.85398169495316
x15 = 52.7338764603268
x16 = 69.7882368066005
x17 = 20.4203521965023
x18 = -23.5619449416433
x19 = 92.2281843477919
x20 = -63.0562527372411
x21 = 84.1498033202441
x22 = 94.023380097403
x23 = -3.81479101884417
x24 = -29.8451300798499
x25 = -28.0499343652511
x26 = 66.1978452470166
x27 = 82.3546073657633
x28 = 95.8185759802228
x29 = -67.5442420672257
x30 = 41.9627019069089
x31 = -18.1763574464374
x32 = 86.8425968691975
x33 = -39.7187071414127
x34 = 85.9449990677518
x35 = -44.2066966123235
x36 = 48.2458871832247
x37 = -13.6883680280288
x38 = -72.0322315269287
x39 = -75.6226232189275
x40 = 4.26359002020643
x41 = 12.3419710894768
x42 = 28.4987335331749
x43 = -31.6403260657234
x44 = 59.9146599502416
x45 = 24.0107438382386
x46 = 43.7578975329286
x47 = -54.0802734815868
x48 = -57.6706651859628
x49 = 74.2762262919595
x50 = -38.8211093539582
x51 = -21.7667490867332
x52 = 61.709855798655
x53 = 2.46839424485093
x54 = -34.33311961254
x55 = 76.0714219867554
x56 = 25.8059396877581
x57 = -62.1586545882655
x58 = 72.4810305791346
x59 = 6.05878569168424
x60 = 13.2395690634871
x61 = 90.4329884842009
x62 = -49.5922838608809
x63 = 11.4443733932631
x64 = -0.224399514512687
x65 = -10.0979763266333
x66 = 67.9930410105944
x67 = -70.2370358625256
x68 = 33.8843208261029
x69 = 15.9323627936885
x70 = -63.9538505397178
x71 = -19.9715533428935
x72 = 40.1675061533025
x73 = 51.8362788401232
x74 = -91.7793853558147
x75 = -89.9841895997492
x76 = 46.4506913541324
x77 = -81.0082105020289
x78 = -2.01959525710412
x79 = -85.4962001961162
x80 = -41.5139028204363
x81 = 31.1915270258916
x82 = -98.0625706387998
x83 = 56.3242682463445
x84 = -99.8577664110223
x85 = 64.4026493415306
x86 = 38.3723102119433
x87 = 22.215548079095
x88 = -93.574581231161
x89 = -46.001892425326
x90 = -26.254738653815
x91 = 100.306565404686
x91 = 100.306565404686