Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation e^x=0
-
Equation 1-5*x=-6*x+8
-
Equation 10*(x-9)=7
-
Equation cos(x)=3
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-4*y=-20
- -9*x-15*y=-4
- 18*x-11*y=2
- Graphing y =:
-
sin(3x)
- Canonical form:
- sin(3x)
- Integral of d{x}:
-
sin(3x)
-
Identical expressions
- sin(3x)= zero
- sinus of (3x) equally 0
- sinus of (3x) equally zero
- sin3x=0
- sin(3x)=O
-
Similar expressions
- 2sin3x+5cos3x=2
sin(3x)=0 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 = -33.5103216382911
x3 = -63.8790506229925
x4 = 94.2477796076938
x5 = -35.6047167406843
x6 = -79.5870138909414
x7 = 569.675467850949
x8 = 109.955742875643
x9 = -4.18879020478639
x10 = 65.9734457253857
x11 = -46.0766922526503
x12 = -15.707963267949
x13 = 90.0589894029074
x14 = 98.4365698124802
x15 = 81.6814089933346
x16 = -85.870199198121
x17 = 6.28318530717959
x18 = 30.3687289847013
x19 = -57.5958653158129
x20 = -31.4159265358979
x21 = 746.651854003174
x22 = 61.7846555205993
x23 = 70.162235930172
x24 = 78.5398163397448
x25 = -87.9645943005142
x26 = 76.4454212373516
x27 = -92.1533845053006
x28 = -72.2566310325652
x29 = -70.162235930172
x30 = 39.7935069454707
x31 = -37.6991118430775
x32 = 4.18879020478639
x33 = -61.7846555205993
x34 = 24.0855436775217
x35 = -39.7935069454707
x36 = -17.8023583703422
x37 = 72.2566310325652
x38 = 8.37758040957278
x39 = -99.4837673636768
x40 = 68.0678408277789
x41 = -90.0589894029074
x42 = 54.4542726622231
x43 = -6.28318530717959
x44 = 85.870199198121
x45 = -8.37758040957278
x46 = -19.8967534727354
x47 = 17.8023583703422
x48 = 46.0766922526503
x49 = 100.530964914873
x50 = -11.5191730631626
x51 = 0.0
x52 = -65.9734457253857
x53 = -21.9911485751286
x54 = -77.4926187885482
x55 = 92.1533845053006
x56 = 19.8967534727354
x57 = -13.6135681655558
x58 = 50.2654824574367
x59 = -26.1799387799149
x60 = 43.9822971502571
x61 = 63.8790506229925
x62 = 74.3510261349584
x63 = 52.3598775598299
x64 = -83.7758040957278
x65 = 15.707963267949
x66 = 28.2743338823081
x67 = 10.471975511966
x68 = 21.9911485751286
x69 = -2.0943951023932
x70 = -68.0678408277789
x71 = 37.6991118430775
x72 = 59.6902604182061
x73 = -28.2743338823081
x74 = -54.4542726622231
x75 = 80.634211442138
x76 = -10.471975511966
x77 = -59.6902604182061
x78 = -41.8879020478639
x79 = 56.5486677646163
x80 = -24.0855436775217
x81 = 2.0943951023932
x82 = 34.5575191894877
x83 = -81.6814089933346
x84 = 41.8879020478639
x85 = 87.9645943005142
x86 = -43.9822971502571
x87 = 32.4631240870945
x88 = 96.342174710087
x89 = -94.2477796076938
x90 = 26.1799387799149
x91 = -98.4365698124802
x92 = -29.3215314335047
x93 = 83.7758040957278
x94 = 48.1710873550435
x95 = -55.5014702134197
x96 = -48.1710873550435
x96 = -48.1710873550435
The graph