Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+6)(2x+6)-20=0
-
Equation 2x^2-9x+15=0
- Equation arctg(x/y)
-
Equation sinx=1/3
- Express {x} in terms of y where:
- -10*x+18*y=6
- 9*x-18*y=6
- -1*x+19*y=-10
- 4*x+13*y=13
- Sum of series:
- sinx
-
1/3
- Graphing y =:
- sinx
- Integral of d{x}:
-
sinx
- Derivative of:
-
1/3
- Limit of the function:
- 1/3
-
Identical expressions
- sinx= one / three
- sinus of x equally 1 divide by 3
- sinus of x equally one divide by three
- sinx=1 divide by 3
-
Similar expressions
- sin(x+(3pi/4))=0
- cos(pi*(x-1)/3)=1/2
sinx=1/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = \frac{1}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
Or
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi - asin(1/3)
$$x_{1} = - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
x2 = asin(1/3)
$$x_{2} = \operatorname{asin}{\left(\frac{1}{3} \right)}$$
Sum and product of roots
[src]
sum
0 + pi - asin(1/3) + asin(1/3)
$$\operatorname{asin}{\left(\frac{1}{3} \right)} + \left(0 + \left(- \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right)\right)$$
=
pi
$$\pi$$
product
1*(pi - asin(1/3))*asin(1/3)
$$1 \left(- \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$
=
(pi - asin(1/3))*asin(1/3)
$$\left(- \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$
(pi - asin(1/3))*asin(1/3)
Numerical answer
[src]
x1 = -34.8973560989418
x2 = -16.0478001774031
x3 = -53.7469120204806
x4 = -62.4920161623417
x5 = 46.7840528943928
x6 = -81.3415720838805
x7 = 82.0212459027887
x8 = -78.879653249199
x9 = -112585.595763607
x10 = 44.3221340597112
x11 = -56.2088308551622
x12 = 100.870801824328
x13 = 90.7663500446499
x14 = 59.350423508752
x15 = 94.5876165171479
x16 = 75.7380605956092
x17 = 25.4725781381725
x18 = 97.0495353518295
x19 = -3.48142956304392
x20 = 69.4548752884296
x21 = 12.9062075238133
x22 = -60.0300973276602
x23 = -12.2265337049051
x24 = -31.0760896264438
x25 = -18.5097190120846
x26 = -68.7752014695213
x27 = 65.6336088159315
x28 = -72.5964679420194
x29 = 88.3044312099683
x30 = 172.447759037984
x31 = 78.1999794302907
x32 = 9.08494105131526
x33 = 0.339836909454122
x34 = -9.7646148702235
x35 = 34.2176822800336
x36 = 2.80175574413567
x37 = -87.6247573910601
x38 = -5.94334839772546
x39 = 53.0672382015724
x40 = 84.4831647374703
x41 = -75.0583867767009
x42 = 38.0389487525316
x43 = -41.1805414061214
x44 = -85.1628385563785
x45 = -37.3592749336234
x46 = 40.5008675872132
x47 = -47.463726713301
x48 = 15.3681263584948
x49 = -66.3132826348398
x50 = -24.7929043192642
x51 = 50.6053193668908
x52 = -93.9079426982397
x53 = -100.191128005419
x54 = 63.17168998125
x55 = 71.9167941231111
x56 = 19.1893928309929
x57 = 6.62302221663371
x58 = -43.642460240803
x59 = 21.6513116656744
x60 = -28.6141707917623
x61 = -97.7292091707377
x62 = -22.3309854845827
x63 = -91.4460238635581
x64 = 951.562737128253
x65 = 31.7557634453521
x66 = 56.8885046740704
x67 = -116.578765092276
x68 = -49.9256455479826
x69 = 27.934496972854
x69 = 27.934496972854
The graph