Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation ((1/5))^(x)^(2)*5^(2*x+2)=(1/5)^(6)
-
Equation x^3-x^2-x-1=0
-
Equation -x=3
-
Equation x-6/2-x/3=3
- Express {x} in terms of y where:
- 9*x+10*y=5
- -4*x+19*y=-13
- -5*x-6*y=-1
- -7*x+15*y=18
- Derivative of:
- -1/2
- Integral of d{x}:
-
-1/2
- Limit of the function:
- -1/2
-
Identical expressions
- sin(pi*x)/ three =- one / two
- sinus of ( Pi multiply by x) divide by 3 equally minus 1 divide by 2
- sinus of ( Pi multiply by x) divide by three equally minus one divide by two
- sin(pix)/3=-1/2
- sinpix/3=-1/2
- sin(pi*x) divide by 3=-1 divide by 2
-
Similar expressions
- sin(pi*x)/3=+1/2
- (6x-4)/3-(3x-2)/6=(2x-1)/2
- (x-1)/(2x+3)-(2x-1)/(3-2x)=0
sin(pi*x)/3=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(pi*x)
--------- = -1/2
3
$$\frac{\sin{\left(\pi x \right)}}{3} = - \frac{1}{2}$$
Detail solution
Given the equation
$$\frac{\sin{\left(\pi x \right)}}{3} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\pi x \right)} = - \frac{3}{2}$$
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\frac{\sin{\left(\pi x \right)}}{3} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\sin{\left(\pi x \right)} = - \frac{3}{2}$$
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.
Sum and product of roots
[src]
sum
pi + re(asin(3/2)) I*im(asin(3/2)) re(asin(3/2)) I*im(asin(3/2))
------------------ + --------------- + - ------------- - ---------------
pi pi pi pi
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right) + \left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right)$$
=
pi + re(asin(3/2)) re(asin(3/2))
------------------ - -------------
pi pi
$$- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi}{\pi}$$
product
/pi + re(asin(3/2)) I*im(asin(3/2))\ / re(asin(3/2)) I*im(asin(3/2))\ |------------------ + ---------------|*|- ------------- - ---------------| \ pi pi / \ pi pi /
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right) \left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right)$$
=
-(I*im(asin(3/2)) + re(asin(3/2)))*(pi + I*im(asin(3/2)) + re(asin(3/2)))
--------------------------------------------------------------------------
2
pi
$$- \frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)}{\pi^{2}}$$
-(i*im(asin(3/2)) + re(asin(3/2)))*(pi + i*im(asin(3/2)) + re(asin(3/2)))/pi^2
Rapid solution
[src]
pi + re(asin(3/2)) I*im(asin(3/2))
x1 = ------------------ + ---------------
pi pi
$$x_{1} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}$$
re(asin(3/2)) I*im(asin(3/2))
x2 = - ------------- - ---------------
pi pi
$$x_{2} = - \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}$$
x2 = -re(asin(3/2))/pi - i*im(asin(3/2))/pi
Numerical answer
[src]
x1 = 1.5 - 0.306348962530033*i
x2 = -0.5 + 0.306348962530033*i
x2 = -0.5 + 0.306348962530033*i