Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation tan(x)=0
-
Equation 4x=24+x
-
Equation x+3=-9x
-
Equation (x-2)^2+(x-3)^2=2x^2
- Express {x} in terms of y where:
- 17*x-18*y=10
- -12*x-3*y=-9
- 4*x+16*y=6
- sin(xy)+cos(xy)=tg(x+y)
- Graphing y =:
-
sin(x+pi/3)
- Integral of d{x}:
-
sin(x+pi/3)
-
Identical expressions
- sin(x+pi/ three)= zero
- sinus of (x plus Pi divide by 3) equally 0
- sinus of (x plus Pi divide by three) equally zero
- sinx+pi/3=0
- sin(x+pi/3)=O
- sin(x+pi divide by 3)=0
-
Similar expressions
- 2*sqrt(3)*sin((x+pi)/3)-cos(2*x)=3*cos(x)-1
- sin(x+(pi/3))=sqrt(2)/2
- 2sin(x+(pi/3))+sqrt(3)=0
- sin(x-pi/3)=0
-
What you mean?
- sin((x + pi)/3) = 0
- sin(x + pi/3) = 0
- sin(x + pi/3) = 0
You entered:
sin(x+pi/3)=0
What you mean?
sin(x+pi/3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x + \frac{\pi}{3} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(x + \frac{\pi}{3} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n$$
$$x + \frac{\pi}{3} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
$$\sin{\left(x + \frac{\pi}{3} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(x + \frac{\pi}{3} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Or
$$x + \frac{\pi}{3} = 2 \pi n$$
$$x + \frac{\pi}{3} = 2 \pi n + \pi$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
Rapid solution
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
Sum and product of roots
[src]
sum
pi 2*pi
0 - -- + ----
3 3
$$\left(- \frac{\pi}{3} + 0\right) + \frac{2 \pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
-pi 2*pi 1*----*---- 3 3
$$\frac{2 \pi}{3} \cdot 1 \left(- \frac{\pi}{3}\right)$$
=
2 -2*pi ------ 9
$$- \frac{2 \pi^{2}}{9}$$
-2*pi^2/9
Numerical answer
[src]
x1 = -76.4454212373516
x2 = -63.8790506229925
x3 = -57.5958653158129
x4 = -98.4365698124802
x5 = 24.0855436775217
x6 = 42.9350995990605
x7 = -70.162235930172
x8 = -4939.63084899435
x9 = -79.5870138909414
x10 = 74.3510261349584
x11 = -16.7551608191456
x12 = 64.9262481741891
x13 = 5.23598775598299
x14 = -73.3038285837618
x15 = -32.4631240870945
x16 = 68.0678408277789
x17 = 14.6607657167524
x18 = -29.3215314335047
x19 = -35.6047167406843
x20 = -154.985237577096
x21 = 27.2271363311115
x22 = -45.0294947014537
x23 = -51.3126800086333
x24 = -95.2949771588904
x25 = 52.3598775598299
x26 = -92.1533845053006
x27 = 61.7846555205993
x28 = 80.634211442138
x29 = -10.471975511966
x30 = -38.7463093942741
x31 = -23.0383461263252
x32 = 77.4926187885482
x33 = -41.8879020478639
x34 = 33.5103216382911
x35 = 8.37758040957278
x36 = -26.1799387799149
x37 = 20.943951023932
x38 = 90.0589894029074
x39 = -82.7286065445312
x40 = 102.625360017267
x41 = -1.0471975511966
x42 = 86.9173967493176
x43 = -48.1710873550435
x44 = 55.5014702134197
x45 = 71.2094334813686
x46 = -60.7374579694027
x47 = 39.7935069454707
x48 = 99.4837673636768
x49 = 2.0943951023932
x50 = -19.8967534727354
x51 = -7.33038285837618
x52 = 96.342174710087
x53 = 17.8023583703422
x54 = -67.0206432765823
x55 = 58.6430628670095
x56 = 30.3687289847013
x57 = -85.870199198121
x58 = -54.4542726622231
x59 = -13.6135681655558
x60 = 11.5191730631626
x61 = -89.0117918517108
x62 = 49.2182849062401
x63 = 36.6519142918809
x64 = 83.7758040957278
x65 = 93.2005820564972
x66 = 46.0766922526503
x67 = -4.18879020478639
x67 = -4.18879020478639
The graph