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Equation:
Equation 4(x-6)=x-9
Equation 3x+3=5x
Equation x/4+x=4
Equation x^2+11=0
Express {x} in terms of y where:
7*x-1*y=-7
-11*x+9*y=-20
13*x-12*y=19
15*x-3*y=-8
Derivative of:
sin(x)
Integral of d{x}:
sin(x)
pi/3
Canonical form:
sin(x)
Identical expressions
sin(x)=pi/ three
sinus of (x) equally Pi divide by 3
sinus of (x) equally Pi divide by three
sinx=pi/3
sin(x)=pi divide by 3
Similar expressions
2sin*x/2=√3
sinx(2sinx-1)=0
sinx=cosx
sinx=pi/3

sin(x)=pi/3 equation

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

The solution

You have entered [src]

         pi
sin(x) = --
         3

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

Simplify

Detail solution

Given the equation

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

- this is the simplest trigonometric equation
As right part of the equation
modulo =

True

but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

       /    /pi\\       /    /pi\\       /    /pi\\     /    /pi\\
pi - re|asin|--|| - I*im|asin|--|| + I*im|asin|--|| + re|asin|--||
       \    \3 //       \    \3 //       \    \3 //     \    \3 //

\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)

pi

\pi

product

/       /    /pi\\       /    /pi\\\ /    /    /pi\\     /    /pi\\\
|pi - re|asin|--|| - I*im|asin|--|||*|I*im|asin|--|| + re|asin|--|||
\       \    \3 //       \    \3 /// \    \    \3 //     \    \3 ///

\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)

 /    /    /pi\\     /    /pi\\\ /          /    /pi\\     /    /pi\\\
-|I*im|asin|--|| + re|asin|--|||*|-pi + I*im|asin|--|| + re|asin|--|||
 \    \    \3 //     \    \3 /// \          \    \3 //     \    \3 ///

- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)

-(i*im(asin(pi/3)) + re(asin(pi/3)))*(-pi + i*im(asin(pi/3)) + re(asin(pi/3)))

Rapid solution [src]

            /    /pi\\       /    /pi\\
x1 = pi - re|asin|--|| - I*im|asin|--||
            \    \3 //       \    \3 //

x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}

         /    /pi\\     /    /pi\\
x2 = I*im|asin|--|| + re|asin|--||
         \    \3 //     \    \3 //

x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}

x2 = re(asin(pi/3)) + i*im(asin(pi/3))

Numerical answer [src]

x1 = 1.5707963267949 + 0.306042108613266*i

x2 = 1.5707963267949 - 0.306042108613266*i

x2 = 1.5707963267949 - 0.306042108613266*i

The graph

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Identical expressions

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sin(x)=pi/3 equation

Numerical solution:

The solution