Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation x-y=1
-
Equation (x+2)/9=(x-3)/2
-
Equation x^2-4x+5=0
-
Equation x^3=27
- Express {x} in terms of y where:
- -11*x+15*y=7
- 4*x+2*y=5
- 1*x+10*y=-18
- -17*x+1*y=-11
- Graphing y =:
- sin(x-pi/3)
- Integral of d{x}:
-
sin(x-pi/3)
-
Identical expressions
- sin(x-pi/ three)= zero
- sinus of (x minus Pi divide by 3) equally 0
- sinus of (x minus Pi divide by three) equally zero
- sinx-pi/3=0
- sin(x-pi/3)=O
- sin(x-pi divide by 3)=0
-
Similar expressions
- sin(x+pi/3)=0
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:
$$\sin{\left(x - \frac{\pi}{3} \right)} = 0$$
The equation is transformed to
$$\cos{\left(x + \frac{\pi}{6} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{6} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
$$\sin{\left(x - \frac{\pi}{3} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(x - \frac{\pi}{3} \right)} = 0$$
Divide both parts of the equation by -1
The equation is transformed to
$$\cos{\left(x + \frac{\pi}{6} \right)} = 0$$
This equation is transformed to
$$x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$x + \frac{\pi}{6} = \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{6} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$x = \pi n + \frac{\pi}{3}$$
$$x = \pi n - \frac{2 \pi}{3}$$
Rapid solution
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
4*pi
x2 = ----
3
$$x_{2} = \frac{4 \pi}{3}$$
x2 = 4*pi/3
Sum and product of roots
[src]
sum
pi 4*pi -- + ---- 3 3
$$\frac{\pi}{3} + \frac{4 \pi}{3}$$
=
5*pi ---- 3
$$\frac{5 \pi}{3}$$
product
pi 4*pi --*---- 3 3
$$\frac{\pi}{3} \frac{4 \pi}{3}$$
=
2 4*pi ----- 9
$$\frac{4 \pi^{2}}{9}$$
4*pi^2/9
Numerical answer
[src]
x1 = 45.0294947014537
x2 = -17.8023583703422
x3 = 38.7463093942741
x4 = -33.5103216382911
x5 = -77.4926187885482
x6 = 89.0117918517108
x7 = -24.0855436775217
x8 = -86.9173967493176
x9 = -49.2182849062401
x10 = 92.1533845053006
x11 = 51.3126800086333
x12 = 23.0383461263252
x13 = -14.6607657167524
x14 = 19.8967534727354
x15 = -99.4837673636768
x16 = -74.3510261349584
x17 = -30.3687289847013
x18 = -20.943951023932
x19 = 41.8879020478639
x20 = -46.0766922526503
x21 = -90.0589894029074
x22 = 57.5958653158129
x23 = 63.8790506229925
x24 = 67.0206432765823
x25 = 54.4542726622231
x26 = -93.2005820564972
x27 = 35.6047167406843
x28 = -5.23598775598299
x29 = 73.3038285837618
x30 = 98.4365698124802
x31 = 32.4631240870945
x32 = 60.7374579694027
x33 = 104.71975511966
x34 = -83.7758040957278
x35 = -71.2094334813686
x36 = 85.870199198121
x37 = 10.471975511966
x38 = -42.9350995990605
x39 = -27.2271363311115
x40 = -8.37758040957278
x41 = 16.7551608191456
x42 = 26.1799387799149
x43 = -96.342174710087
x44 = -58.6430628670095
x45 = 29.3215314335047
x46 = 13.6135681655558
x47 = -2.0943951023932
x48 = -36.6519142918809
x49 = -64.9262481741891
x50 = -52.3598775598299
x51 = -68.0678408277789
x52 = 1.0471975511966
x53 = 70.162235930172
x54 = 76.4454212373516
x55 = 79.5870138909414
x56 = 48.1710873550435
x57 = 95.2949771588904
x58 = -55.5014702134197
x59 = 82.7286065445312
x60 = -80.634211442138
x61 = 7.33038285837618
x62 = -5644.39480094966
x63 = -11.5191730631626
x64 = 4.18879020478639
x65 = -61.7846555205993
x66 = -39.7935069454707
x66 = -39.7935069454707
The graph