Mister Exam

Lang:

How to use it?
Equation:
Equation (x-2)^2*(x-3)=12*(x-2)
Equation x-y+2=0
Equation x*8=25+15
Equation (x-11)*(-x+9)=0
Express {x} in terms of y where:
-6*x-10*y=19
6*x+17*y=-11
-13*x+7*y=-15
-4*x-8*y=-20
Integral of d{x}:
sin(x+(pi/3))
Limit of the function:
sqrt(2)/2
sqrt(2)/2
Identical expressions
sin(x+(pi/ three))=sqrt(two)/ two
sinus of (x plus ( Pi divide by 3)) equally square root of (2) divide by 2
sinus of (x plus ( Pi divide by three)) equally square root of (two) divide by two
sin(x+(pi/3))=√(2)/2
sinx+pi/3=sqrt2/2
sin(x+(pi divide by 3))=sqrt(2) divide by 2
Similar expressions
4*sin(x+pi/3)+cos(2*x+2*pi/3)=5/2
2*sin(x+pi/3)=sqrt(3)
sin(x+pi/3)=1/2
3*ctg(pi/3)*sin(x+pi/3)-sqrt(3)=0
sin(x-(pi/3))=sqrt(2)/2

sin(x+(pi/3))=sqrt(2)/2 equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

                ___
   /    pi\   \/ 2 
sin|x + --| = -----
   \    3 /     2

\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{2}}{2}

Simplify

Detail solution

Given the equation

\sin{\left(x + \frac{\pi}{3} \right)} = \frac{\sqrt{2}}{2}

- this is the simplest trigonometric equation
This equation is transformed to

x + \frac{\pi}{3} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}

x + \frac{\pi}{3} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi

x + \frac{\pi}{3} = 2 \pi n + \frac{\pi}{4}

x + \frac{\pi}{3} = 2 \pi n + \frac{3 \pi}{4}

, 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}{12}

x = 2 \pi n + \frac{5 \pi}{12}

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     -pi 
x1 = ----
      12

x_{1} = - \frac{\pi}{12}

     5*pi
x2 = ----
      12

x_{2} = \frac{5 \pi}{12}

x2 = 5*pi/12

Sum and product of roots [src]

sum

  pi   5*pi
- -- + ----
  12    12

- \frac{\pi}{12} + \frac{5 \pi}{12}

pi
--
3

\frac{\pi}{3}

product

-pi  5*pi
----*----
 12   12

- \frac{\pi}{12} \frac{5 \pi}{12}

     2
-5*pi 
------
 144

- \frac{5 \pi^{2}}{144}

-5*pi^2/144

Numerical answer [src]

x1 = 56.2868683768171

x2 = -55.2396708256205

x3 = 31.1541271480988

x4 = 81.4196096055355

x5 = 18.5877565337396

x6 = -25.3945406165175

x7 = 70.4240353179712

x8 = 75.1364242983559

x9 = 45.2912940892529

x10 = -30.1069295969022

x11 = -74.0892267471593

x12 = 12.30457122656

x13 = 100.269165527074

x14 = 39.0081087820733

x15 = -80.3724120543389

x16 = -69.3768377667746

x17 = 50.0036830696375

x18 = -11.2573736753634

x19 = -56.8104671524154

x20 = 57.857664703612

x21 = 8639.11799798413

x22 = 87.7027949127151

x23 = -36.3901149040818

x24 = -19.1113553093379

x25 = -281.434341884086

x26 = 26.4417381677141

x27 = -94.5095789954929

x28 = -17.540558982543

x29 = -4.97418836818384

x30 = -92.9387826686981

x31 = 82.9904059323304

x32 = 89.27359123951

x33 = -88.2263936883134

x34 = -44.2440965380563

x35 = 7.59218224617533

x36 = 6.02138591938044

x37 = -75.6600230739542

x38 = 24.8709418409192

x39 = -23.8237442897226

x40 = -86.6555973615185

x41 = -67.8060414399797

x42 = -37.9609112308767

x43 = -12.8281700021583

x44 = -48.9564855184409

x45 = -0.261799387799149

x46 = 95.5567765466895

x47 = -42.6733002112614

x48 = 1.30899693899575

x49 = 20.1585528605345

x50 = -50.5272818452358

x51 = 43.720497762458

x52 = 68.8532389911763

x53 = 13.8753675533549

x54 = 32.7249234748937

x55 = 37.4373124552784

x56 = 51.5744793964324

x57 = 64.1408500107916

x58 = 62.5700536839967

x59 = -6.54498469497874

x60 = -31.6777259236971

x61 = -81.9432083811338

x62 = -61.5228561328001

x63 = 93.9859802198946

x64 = -63.093652459595

x65 = 108.123147161049

x66 = -99.2219679758776

x67 = 76.7072206251508

x67 = 76.7072206251508