Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 64-x^2=0
- Equation (x^2+a)/x+x/(x^2+a)=-5/2
-
Equation 16x^2-1=0
-
Equation x^2-6x+13=0
- Express {x} in terms of y where:
- -8*x-2*y=-11
- -14*x-7*y=-10
- -20*x-12*y=-17
- 3*x+8*y=-7
- Derivative of:
-
2*sin(5*x)
- -4
- Integral of d{x}:
-
-4
- Limit of the function:
- -4
-
Identical expressions
- two *sin(five *x)=- four
- 2 multiply by sinus of (5 multiply by x) equally minus 4
- two multiply by sinus of (five multiply by x) equally minus four
- 2sin(5x)=-4
- 2sin5x=-4
-
Similar expressions
- 1/2*(sin(5*x-x)+sin(5*x+x))*1/2*(sin(x-5*x)+sin(x+5*x))=0
- 2*sin(5*x)=+4
- x*sqrt(x-a)=sqrt(4*x^2-(4*a+2)*x+2*a)
- y=C1*cos(5x)+C2*sin(5x)
- -(4x-7)=-7x
- 2*(sin(5x))*(sin((3x)/2))=sin(x/2)
- (√2+2cos7x)(2sin5x+1)=0
2*sin(5*x)=-4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(5 x \right)} = -4$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(5 x \right)} = -2$$
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.
$$2 \sin{\left(5 x \right)} = -4$$
- 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.
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