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Equation:
Equation tan(x)=0
Equation x^2-7x+6=0
Equation ctgx=-1
Equation (m+8)*(m-7)=0
Express {x} in terms of y where:
-1*x-7*y=5
-4*x-18*y=-14
1*x+7*y=8
1*x+19*y=-10
Integral of d{x}:
sinx/4
Derivative of:
sinx/4
Identical expressions
sinx/ four =-sqrt two /2
sinus of x divide by 4 equally minus square root of 2 divide by 2
sinus of x divide by four equally minus square root of two divide by 2
sinx/4=-√2/2
sinx divide by 4=-sqrt2 divide by 2
Similar expressions
cos*((pi*(2*x+6))/4)=-(sqrt2/2)
sinx/4=+sqrt2/2
cos(2*x)*(2*cos(7*x))+cos(5*x+pi)=-sqrt(2)/2
1+6*sin(x/4)*cos(x/4)=0
sin(x/4-pi/8)=0
sin(x/4)=1/2sqrt(5,5/30)
6*sin(x/4-pi/12)-6=0
cos(pi(4×x+108)/4)=-sqrt(2)/2
sqrt(2)*sin(2*x)*sin(x-pi/4)=2*(-sqrt(2)/2)

sinx/4=-sqrt2/2 equation

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

The solution

You have entered [src]

            ___ 
sin(x)   -\/ 2  
------ = -------
  4         2

\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{2}}{2}

Simplify

Detail solution

Given the equation

\frac{\sin{\left(x \right)}}{4} = \frac{\left(-1\right) \sqrt{2}}{2}

- this is the simplest trigonometric equation

Divide both parts of the equation by 1/4

The equation is transformed to

\sin{\left(x \right)} = - 2 \sqrt{2}

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

             /    /    ___\\     /    /    ___\\       /    /    ___\\       /    /    ___\\
0 + pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 // + - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //

\left(0 + \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)\right) - \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)

pi

\pi

product

  /         /    /    ___\\     /    /    ___\\\ /    /    /    ___\\       /    /    ___\\\
1*\pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\- re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 ///

\left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) 1 \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)

 /    /    /    ___\\     /    /    ___\\\ /         /    /    ___\\     /    /    ___\\\
-\I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///

- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)

-(i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))*(pi + i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))

Rapid solution [src]

              /    /    ___\\     /    /    ___\\
x1 = pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 //

x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}

Simplify

         /    /    ___\\       /    /    ___\\
x2 = - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //

x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}

Simplify

Numerical answer [src]

x1 = 4.71238898038469 - 1.70004220705667*i

x2 = -1.5707963267949 + 1.70004220705667*i

x2 = -1.5707963267949 + 1.70004220705667*i

The graph

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sinx/4=-sqrt2/2 equation

Numerical solution:

The solution