Mister Exam

Other calculators

sin(x)=-2

sin(x)=-2 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] 
sin(x) = -2
sin⁡(x)=−2\sin{\left(x \right)} = -2
Simplify
Detail solution
Given the equation
sin⁡(x)=−2\sin{\left(x \right)} = -2
- 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
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 + pi + I*im(asin(2)) + re(asin(2)) + -re(asin(2)) - I*im(asin(2))
(0+(re⁡(asin⁡(2))+π+iim⁡(asin⁡(2))))−(re⁡(asin⁡(2))+iim⁡(asin⁡(2)))\left(0 + \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)\right) - \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 
=
pi
π\pi 
product
1*(pi + I*im(asin(2)) + re(asin(2)))*(-re(asin(2)) - I*im(asin(2)))
(−re⁡(asin⁡(2))−iim⁡(asin⁡(2)))1(re⁡(asin⁡(2))+π+iim⁡(asin⁡(2)))\left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 1 \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 
=
-(I*im(asin(2)) + re(asin(2)))*(pi + I*im(asin(2)) + re(asin(2)))
−(re⁡(asin⁡(2))+iim⁡(asin⁡(2)))(re⁡(asin⁡(2))+π+iim⁡(asin⁡(2)))- \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) 
-(i*im(asin(2)) + re(asin(2)))*(pi + i*im(asin(2)) + re(asin(2)))
Rapid solution [src] 
x1 = pi + I*im(asin(2)) + re(asin(2))
x1=re⁡(asin⁡(2))+π+iim⁡(asin⁡(2))x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}
Simplify 
x2 = -re(asin(2)) - I*im(asin(2))
x2=−re⁡(asin⁡(2))−iim⁡(asin⁡(2))x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}
Simplify
Numerical answer [src] 
x1 = 4.71238898038469 - 1.31695789692482*i
x2 = -1.5707963267949 + 1.31695789692482*i
x2 = -1.5707963267949 + 1.31695789692482*i
The graph
sin(x)=-2 equation
    © Mister Exam – Calculator