Mister Exam

Other calculators

2*sin(5*x)=-4 equation

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

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
2*sin(5*x) = -4
$$2 \sin{\left(5 x \right)} = -4$$
Detail solution
Given the equation
$$2 \sin{\left(5 x \right)} = -4$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2

The equation is transformed to
$$\sin{\left(5 x \right)} = -2$$
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
Rapid solution [src]
     pi   re(asin(2))   I*im(asin(2))
x1 = -- + ----------- + -------------
     5         5              5      
$$x_{1} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} + \frac{\pi}{5} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}$$
       re(asin(2))   I*im(asin(2))
x2 = - ----------- - -------------
            5              5      
$$x_{2} = - \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}$$
x2 = -re(asin(2))/5 - i*im(asin(2))/5
Sum and product of roots [src]
sum
pi   re(asin(2))   I*im(asin(2))     re(asin(2))   I*im(asin(2))
-- + ----------- + ------------- + - ----------- - -------------
5         5              5                5              5      
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} + \frac{\pi}{5} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}\right) + \left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}\right)$$
=
pi
--
5 
$$\frac{\pi}{5}$$
product
/pi   re(asin(2))   I*im(asin(2))\ /  re(asin(2))   I*im(asin(2))\
|-- + ----------- + -------------|*|- ----------- - -------------|
\5         5              5      / \       5              5      /
$$\left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}\right) \left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5} + \frac{\pi}{5} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}}{5}\right)$$
=
-(I*im(asin(2)) + re(asin(2)))*(pi + I*im(asin(2)) + re(asin(2))) 
------------------------------------------------------------------
                                25                                
$$- \frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)}{25}$$
-(i*im(asin(2)) + re(asin(2)))*(pi + i*im(asin(2)) + re(asin(2)))/25
Numerical answer [src]
x1 = 0.942477796076938 - 0.263391579384963*i
x2 = -0.314159265358979 + 0.263391579384963*i
x2 = -0.314159265358979 + 0.263391579384963*i