Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation x^2=-16
-
Equation sin(x)=-1
- Express {x} in terms of y where:
- 4*x-15*y=19
- 16*x-17*y=-9
- 7*x-2*y=20
- -7*x-7*y=-14
- Derivative of:
-
sin(x)
- Integral of d{x}:
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sin(x)
- -1/5
- Canonical form:
- sin(x)
- Limit of the function:
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-1/5
-
Identical expressions
- sin(x)=- one / five
- sinus of (x) equally minus 1 divide by 5
- sinus of (x) equally minus one divide by five
- sinx=-1/5
- sin(x)=-1 divide by 5
-
Similar expressions
- 4*cos^4(x)-4*cos^2(x)+3cosxsinx+1=0
- tg(X)-(1/(5*X))=0
- (6*x-1)/(5-x)=(6*x+3)/9+4/3
- sinx-cosx=0
- sinx=7/10
- sin(x)=+1/5
- sinx=-1/5
sin(x)=-1/5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
$$\sin{\left(x \right)} = - \frac{1}{5}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Or
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, where n - is a integer
Rapid solution
[src]
x1 = pi + asin(1/5)
$$x_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
x2 = -asin(1/5)
$$x_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
x2 = -asin(1/5)
Sum and product of roots
[src]
sum
pi + asin(1/5) - asin(1/5)
$$- \operatorname{asin}{\left(\frac{1}{5} \right)} + \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right)$$
=
pi
$$\pi$$
product
(pi + asin(1/5))*(-asin(1/5))
$$\left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$
=
-(pi + asin(1/5))*asin(1/5)
$$- \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
-(pi + asin(1/5))*asin(1/5)
Numerical answer
[src]
x1 = 41.0420624174576
x2 = -75.5995816069454
x3 = 87.7632363797239
x4 = -44.1836550710474
x5 = 78.7411742605352
x6 = 81.4800510725443
x7 = 100.329606994083
x8 = 28.4756918030985
x9 = -34.3561612686974
x10 = 53.6084330318168
x11 = -69.3163962997658
x12 = -37.9004697638678
x13 = -279.400388248701
x14 = 18.6481980007484
x15 = 75.1968657653647
x16 = 59.8916183389964
x17 = -100.732322835664
x18 = 91.3075448748943
x19 = 3.34295057438012
x20 = -97.1880143404933
x21 = 172.988953868229
x22 = -46.9225318830566
x23 = 62.6304951510055
x24 = 72.4579889533556
x25 = -81.882766914125
x26 = -72.0552731117749
x27 = 129.006656717972
x28 = 9845.55001842962
x29 = 66.174803646176
x30 = -50.466840378227
x31 = 47.3252477246372
x32 = -63.0332109925862
x33 = -65.7720878045953
x34 = -28.0729759615178
x35 = 225.993313137675
x36 = -9.22342003997905
x37 = -12.7677285351495
x38 = 56.3473098438259
x39 = 97.5907301820739
x40 = 85.0243595677148
x41 = -0.201357920790331
x42 = 4024.58154716932
x43 = -56.7500256854066
x44 = -59.4889024974157
x45 = -6.48454322796992
x46 = -90.9048290333137
x47 = 37.4977539222872
x48 = 3845.10805007312
x49 = 24.931383307928
x50 = 43.7809392294668
x51 = -107.015508142843
x52 = 34.7588771102781
x53 = 6.08182738638926
x54 = 22.1925064959189
x55 = -2.94023473279946
x56 = 9.62613588155971
x57 = 68.9136804581851
x58 = -31.6172844566883
x59 = -40.639346575877
x60 = -15.5066053471586
x61 = 50.0641245366464
x62 = -94.4491375284841
x63 = -19.0509138423291
x64 = 12.3650126935688
x65 = -84.6216437261341
x66 = -21.7897906543382
x67 = -53.2057171902362
x68 = -78.3384584189545
x69 = 31.2145686151076
x70 = 94.0464216869035
x71 = -25.3340991495087
x72 = 15.9093211887393
x73 = -88.1659522213045
x73 = -88.1659522213045
The graph