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Equation:
Equation -x=4-3(3x-8)
Equation x/9+x=-10/3
Equation √(x^2-1)=2*x
Equation 4(x-3)=x+6
Express {x} in terms of y where:
-6*x-20*y=8
-9*x-15*y=-4
1*x+5*y=-11
12*x-14*y=20
Derivative of:
-1/2
Limit of the function:
-1/2
Integral of d{x}:
-1/2
Identical expressions
sinpi((x+ eleven)/ six)=- one / two
sinus of Pi ((x plus 11) divide by 6) equally minus 1 divide by 2
sinus of Pi ((x plus eleven) divide by six) equally minus one divide by two
sinpix+11/6=-1/2
sinpi((x+11) divide by 6)=-1 divide by 2
Similar expressions
cos(2*x)=-(1/2)
sinpi((x-11)/6)=-1/2
sinpi((x+11)/6)=+1/2

sinpi((x+11)/6)=-1/2 equation

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

The solution

You have entered [src]

         x + 11       
sin(p)*I*------ = -1/2
           6

$$\frac{x + 11}{6} i \sin{\left(p \right)} = - \frac{1}{2}$$

Simplify

Detail solution

Given the equation
$$\frac{x + 11}{6} i \sin{\left(p \right)} = - \frac{1}{2}$$
transform
$$\frac{i \left(x + 11\right) \sin{\left(p \right)}}{6} - \frac{1}{2} = 0$$
$$\frac{x + 11}{6} i \sin{\left(p \right)} - \frac{1}{2} = 0$$
Do replacement
$$w = \sin{\left(p \right)}$$
Expand brackets in the left part

-1/2 + i*wx/6+11/6 = 0

Looking for similar summands in the left part:

-1/2 + i*w*(11 + x)/6 = 0

Move free summands (without w)
from left part to right part, we given:
$$\frac{i w \left(x + 11\right)}{6} = \frac{1}{2}$$
Divide both parts of the equation by i*(11 + x)/6

w = 1/2 / (i*(11 + x)/6)

We get the answer: w = -3*i/(11 + x)
do backward replacement
$$\sin{\left(p \right)} = w$$
substitute w:

The graph

Rapid solution [src]

                         3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
x1 = -11 + --------------------------------------------------- + ---------------------------------------------------
              2            2              2           2             2            2              2           2       
           cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))

$$x_{1} = -11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$

x1 = -11 + 3*i*sin(re(p))*cosh(im(p))/(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2) + 3*cos(re(p))*sinh(im(p))/(sin(re(p))^2*cosh(im(p))^2 + cos(re(p))^2*sinh(im(p))^2)

Sum and product of roots [src]

sum

                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))

$$-11 + \frac{3 i \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}} + \frac{3 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \cosh^{2}{\left(\operatorname{im}{\left(p\right)} \right)} + \cos^{2}{\left(\operatorname{re}{\left(p\right)} \right)} \sinh^{2}{\left(\operatorname{im}{\left(p\right)} \right)}}$$

                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))

product

                    3*cos(re(p))*sinh(im(p))                             3*I*cosh(im(p))*sin(re(p))            
-11 + --------------------------------------------------- + ---------------------------------------------------
         2            2              2           2             2            2              2           2       
      cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))   cos (re(p))*sinh (im(p)) + cosh (im(p))*sin (re(p))

-(I*(-3 + 11*cos(re(p))*sinh(im(p))) + 11*cosh(im(p))*sin(re(p))) 
------------------------------------------------------------------
        cosh(im(p))*sin(re(p)) + I*cos(re(p))*sinh(im(p))

$$- \frac{i \left(11 \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)} - 3\right) + 11 \sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)}}{\sin{\left(\operatorname{re}{\left(p\right)} \right)} \cosh{\left(\operatorname{im}{\left(p\right)} \right)} + i \cos{\left(\operatorname{re}{\left(p\right)} \right)} \sinh{\left(\operatorname{im}{\left(p\right)} \right)}}$$

-(i*(-3 + 11*cos(re(p))*sinh(im(p))) + 11*cosh(im(p))*sin(re(p)))/(cosh(im(p))*sin(re(p)) + i*cos(re(p))*sinh(im(p)))

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Identical expressions

Similar expressions

sinpi((x+11)/6)=-1/2 equation

Numerical solution:

The solution