Mister Exam
Other calculators
-
How to use it?
- Equation:
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Equation sin(x)=1/5
-
Equation x^2+11=0
-
Equation x^2+5x+6=0
-
Equation -x/7+x=15/7
- Express {x} in terms of y where:
- 9*x+17*y=13
- 20*x+18*y=-9
- -4*x-8*y=-20
- -1*x+4*y=-10
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
-
1/5
- Canonical form:
- sin(x)
- Sum of series:
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1/5
- Limit of the function:
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1/5
-
Identical expressions
- sin(x)= one / five
- sinus of (x) equally 1 divide by 5
- sinus of (x) equally one divide by five
- sinx=1/5
- sin(x)=1 divide by 5
-
Similar expressions
- sinx(2sinx-1)=0
- 2*sin(x-(pi/4))=1
- 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)
$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
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)
$$\operatorname{asin}{\left(\frac{1}{5} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$
=
pi
$$\pi$$
product
(pi - asin(1/5))*asin(1/5)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
=
(pi - asin(1/5))*asin(1/5)
$$\left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$
(pi - asin(1/5))*asin(1/5)
Numerical answer
[src]
x1 = 56.7500256854066
x2 = -41.0420624174576
x3 = 63.0332109925862
x4 = 97.1880143404933
x5 = -47.3252477246372
x6 = -3.34295057438012
x7 = 2.94023473279946
x8 = 46.9225318830566
x9 = -100.329606994083
x10 = 81.882766914125
x11 = -12.3650126935688
x12 = -62.6304951510055
x13 = 40.639346575877
x14 = -94.0464216869035
x15 = -66.174803646176
x16 = -24.931383307928
x17 = -15.9093211887393
x18 = -75.1968657653647
x19 = 21.7897906543382
x20 = -2814.66565969566
x21 = -28.4756918030985
x22 = -97.5907301820739
x23 = -1746.52415747513
x24 = -59.8916183389964
x25 = 12.7677285351495
x26 = -78.7411742605352
x27 = -85.0243595677148
x28 = -34.7588771102781
x29 = 15.5066053471586
x30 = -348.918142469257
x31 = 53.2057171902362
x32 = 59.4889024974157
x33 = 37.9004697638678
x34 = -9.62613588155971
x35 = -81.4800510725443
x36 = 6.48454322796992
x37 = 84.6216437261341
x38 = 34.3561612686974
x39 = 65.7720878045953
x40 = -18.6481980007484
x41 = -91.3075448748943
x42 = 9.22342003997905
x43 = 69.3163962997658
x44 = -31.2145686151076
x45 = 78.3384584189545
x46 = 25.3340991495087
x47 = -43.7809392294668
x48 = 31.6172844566883
x49 = 100.732322835664
x50 = 88.1659522213045
x51 = -72.4579889533556
x52 = -87.7632363797239
x53 = -68.9136804581851
x54 = 0.201357920790331
x55 = 94.4491375284841
x56 = 72.0552731117749
x57 = -53.6084330318168
x58 = -6.08182738638926
x59 = 28.0729759615178
x60 = 44.1836550710474
x61 = 90.9048290333137
x62 = -188.294201294597
x63 = -56.3473098438259
x64 = -22.1925064959189
x65 = 19.0509138423291
x66 = 75.5995816069454
x67 = 50.466840378227
x68 = -37.4977539222872
x69 = -50.0641245366464
x69 = -50.0641245366464
The graph