Mister Exam

Lang:

How to use it?
Equation:
Equation x^2+4*x-5=0
Equation 2*sin(x)=1
Equation 5x+8=-12
Equation x/9+x=-3
Express {x} in terms of y where:
-12*x-2*y=-15
1*x+11*y=-3
-2*x+2*y=4
8*x-16*y=14
Derivative of:
sqrt(3)
Integral of d{x}:
sqrt(3)
The double integral of:
sqrt(3)
Identical expressions
two *sin(x+pi/ three)=sqrt(three)
2 multiply by sinus of (x plus Pi divide by 3) equally square root of (3)
two multiply by sinus of (x plus Pi divide by three) equally square root of (three)
2*sin(x+pi/3)=√(3)
2sin(x+pi/3)=sqrt(3)
2sinx+pi/3=sqrt3
2*sin(x+pi divide by 3)=sqrt(3)
Similar expressions
sqrt(3*x+1)=x-1
sqrt(x-1)+sqrt(3-x)=2
2*sin((x+pi)/3)+cos(2*x)=sqrt(3)*cos(x)+1
2*sin(x-pi/3)=sqrt(3)

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

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

You have entered [src]

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

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

Simplify

Detail solution

Given the equation

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

- this is the simplest trigonometric equation

Divide both parts of the equation by 2

The equation is transformed to

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

This equation is transformed to

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

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

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

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

, 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

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

The graph

Plot the graph f1(x)

Plot the graph f2(x)

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

Rapid solution [src]

x1 = 0

x_{1} = 0

     pi
x2 = --
     3

x_{2} = \frac{\pi}{3}

x2 = pi/3

Numerical answer [src]

x1 = -18.8495559215388

x2 = 70.162235930172

x3 = -86.9173967493176

x4 = 89.0117918517108

x5 = -17.8023583703422

x6 = 95.2949771588904

x7 = -37.6991118430775

x8 = 82.7286065445312

x9 = -56.5486677646163

x10 = 7.33038285837618

x11 = 76.4454212373516

x12 = 12.5663706143592

x13 = 32.4631240870945

x14 = -31.4159265358979

x15 = 38.7463093942741

x16 = -81.6814089933346

x17 = 94.2477796076938

x18 = 0.0

x19 = -87.9645943005142

x20 = 81.6814089933346

x21 = -75.398223686155

x22 = 62.8318530717959

x23 = -42.9350995990605

x24 = 100.530964914873

x25 = -5.23598775598299

x26 = -30.3687289847013

x27 = 75.398223686155

x28 = 6.28318530717959

x29 = -6.28318530717959

x30 = 57.5958653158129

x31 = 31.4159265358979

x32 = 25.1327412287183

x33 = 13.6135681655558

x34 = 18.8495559215388

x35 = -99.4837673636768

x36 = -94.2477796076938

x37 = 19.8967534727354

x38 = 56.5486677646163

x39 = -20589.9982516275

x40 = -93.2005820564972

x41 = -25.1327412287183

x42 = -49.2182849062401

x43 = 87.9645943005142

x44 = -24.0855436775217

x45 = -50.2654824574367

x46 = -55.5014702134197

x47 = -43.9822971502571

x48 = 50.2654824574367

x49 = 69.1150383789755

x50 = 63.8790506229925

x51 = 1037.77277323583

x52 = -74.3510261349584

x53 = -68.0678408277789

x54 = -62.8318530717959

x55 = -69.1150383789755

x56 = 1.0471975511966

x57 = 51.3126800086333

x58 = -61.7846555205993

x59 = -36.6519142918809

x60 = 37.6991118430775

x61 = -80.634211442138

x62 = -11.5191730631626

x63 = -12.5663706143592

x64 = 45.0294947014537

x65 = 106.814150222053

x66 = 26.1799387799149

x67 = 43.9822971502571

x67 = 43.9822971502571