Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -x^2+5*x-6=0
-
Equation 1/(x-1)^2+2/(x-1)-3=0
-
Equation tan(x)=4
- Equation z^2+3+4*i=0
- Express {x} in terms of y where:
- 10*x-15*y=16
- -18*x-6*y=-1
- -1*x-17*y=-12
- -2*x+20*y=-2
- Derivative of:
-
sin(3*x)
- Integral of d{x}:
-
sin(3*x)
- Limit of the function:
-
sin(3*x)
-
Identical expressions
- sin(three *x)
- sinus of (3 multiply by x)
- sinus of (three multiply by x)
- sin(3x)
- sin3x
-
Similar expressions
- sinx+sin^3x+2020*sin^5x=cos(2x)+cos^3(2x)+2020*cos^5(2x)
- sin23x-3sin3x+2=0
- sin^(3)(x)+3*sin(x)*cos(x)+sin(x)*cos(x)=5cos^(3)(x)
sin(3*x) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$3 x = 2 \pi n$$
$$3 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{3}$$
$$\sin{\left(3 x \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(3 x \right)} = 0$$
This equation is transformed to
$$3 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$3 x = 2 \pi n$$
$$3 x = 2 \pi n + \pi$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{3}$$
Sum and product of roots
[src]
sum
pi -- 3
$$\frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
pi 0*-- 3
$$0 \frac{\pi}{3}$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = -50.2654824574367
x2 = 85.870199198121
x3 = 74.3510261349584
x4 = -41.8879020478639
x5 = -68.0678408277789
x6 = -77.4926187885482
x7 = 72.2566310325652
x8 = -43.9822971502571
x9 = -90.0589894029074
x10 = -99.4837673636768
x11 = -37.6991118430775
x12 = 34.5575191894877
x13 = -94.2477796076938
x14 = 52.3598775598299
x15 = -48.1710873550435
x16 = -21.9911485751286
x17 = 50.2654824574367
x18 = -15.707963267949
x19 = -46.0766922526503
x20 = -2.0943951023932
x21 = 21.9911485751286
x22 = -87.9645943005142
x23 = -72.2566310325652
x24 = -92.1533845053006
x25 = 70.162235930172
x26 = 4.18879020478639
x27 = 59.6902604182061
x28 = 41.8879020478639
x29 = -70.162235930172
x30 = -13.6135681655558
x31 = -85.870199198121
x32 = 48.1710873550435
x33 = -17.8023583703422
x34 = 10.471975511966
x35 = -35.6047167406843
x36 = -55.5014702134197
x37 = -65.9734457253857
x38 = 46.0766922526503
x39 = 15.707963267949
x40 = -83.7758040957278
x41 = 28.2743338823081
x42 = 94.2477796076938
x43 = 63.8790506229925
x44 = 39.7935069454707
x45 = 80.634211442138
x46 = -79.5870138909414
x47 = 37.6991118430775
x48 = 96.342174710087
x49 = 6.28318530717959
x50 = -54.4542726622231
x51 = 569.675467850949
x52 = 83.7758040957278
x53 = -6.28318530717959
x54 = -19.8967534727354
x55 = 8.37758040957278
x56 = -33.5103216382911
x57 = -11.5191730631626
x58 = -61.7846555205993
x59 = -29.3215314335047
x60 = -24.0855436775217
x61 = -10.471975511966
x62 = 0.0
x63 = -39.7935069454707
x64 = 2.0943951023932
x65 = 54.4542726622231
x66 = 17.8023583703422
x67 = -28.2743338823081
x68 = 81.6814089933346
x69 = -26.1799387799149
x70 = 98.4365698124802
x71 = 100.530964914873
x72 = 24.0855436775217
x73 = -8.37758040957278
x74 = 746.651854003174
x75 = 78.5398163397448
x76 = 30.3687289847013
x77 = 92.1533845053006
x78 = -98.4365698124802
x79 = 87.9645943005142
x80 = 32.4631240870945
x81 = 61.7846555205993
x82 = 109.955742875643
x83 = 43.9822971502571
x84 = -31.4159265358979
x85 = -57.5958653158129
x86 = 56.5486677646163
x87 = -81.6814089933346
x88 = -63.8790506229925
x89 = -4.18879020478639
x90 = 68.0678408277789
x91 = 26.1799387799149
x92 = -59.6902604182061
x93 = 65.9734457253857
x94 = 76.4454212373516
x95 = 90.0589894029074
x96 = 19.8967534727354
x96 = 19.8967534727354