Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=4
-
Equation x^2+2x+2=0
-
Equation 3/(x-5)+8/x=2
- Equation z^3+i=0
- Express {x} in terms of y where:
- -1*x-6*y=18
- 6*x-19*y=-18
- -14*x+18*y=0
- -8*x+3*y=-4
- Sum of series:
-
0,1
-
Identical expressions
- sin(x+y)- one , five *x= zero , one
- sinus of (x plus y) minus 1,5 multiply by x equally 0,1
- sinus of (x plus y) minus one , five multiply by x equally zero , one
- sin(x+y)-1,5x=0,1
- sinx+y-1,5x=0,1
- sin(x+y)-1,5*x=O,1
-
Similar expressions
- sin(x-y)-1,5*x=0,1
- sin(x+y)+1,5*x=0,1
sin(x+y)-1,5*x=0,1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
3*x
sin(x + y) - --- = 1/10
2
$$- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}$$
Detail solution
Given the equation
$$- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
Or
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
, where n - is a integer
Move
$$x$$
to right part of the equation
with the opposite sign, in total:
$$y = 2 \pi n - x + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$y = 2 \pi n - x - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
$$- \frac{3 x}{2} + \sin{\left(x + y \right)} = \frac{1}{10}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
Or
$$x + y = 2 \pi n + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$x + y = 2 \pi n - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
, where n - is a integer
Move
$$x$$
to right part of the equation
with the opposite sign, in total:
$$y = 2 \pi n - x + \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}$$
$$y = 2 \pi n - x - \operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)} + \pi$$
The graph
Sum and product of roots
[src]
sum
/ / /1 3*x\\\ / /1 3*x\\ / /1 3*x\\ / / /1 3*x\\\
-re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---|| + pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---|||
\ \ \10 2 /// \ \10 2 // \ \10 2 // \ \ \10 2 ///
$$\left(i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \left(i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi\right)$$
=
/ / /1 3*x\\\ / / /1 3*x\\\
pi - 2*re(x) + I*|-im(x) - im|asin|-- + ---||| + I*|-im(x) + im|asin|-- + ---|||
\ \ \10 2 /// \ \ \10 2 ///
$$i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - 2 \operatorname{re}{\left(x\right)} + \pi$$
product
/ / / /1 3*x\\\ / /1 3*x\\\ / / /1 3*x\\ / / /1 3*x\\\\ |-re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---|||*|pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---|||| \ \ \ \10 2 /// \ \10 2 /// \ \ \10 2 // \ \ \10 2 ////
$$\left(i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) \left(i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi\right)$$
=
/ / /1 3*x\\ / / /1 3*x\\ \ \ / / / /1 3*x\\\ / /1 3*x\\\ |- re|asin|-- + ---|| + I*|- im|asin|-- + ---|| + im(x)| + re(x)|*|-pi + I*|im(x) + im|asin|-- + ---||| + re(x) + re|asin|-- + ---||| \ \ \10 2 // \ \ \10 2 // / / \ \ \ \10 2 /// \ \10 2 ///
$$\left(i \left(\operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) \left(i \left(\operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) + \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} - \pi\right)$$
(-re(asin(1/10 + 3*x/2)) + i*(-im(asin(1/10 + 3*x/2)) + im(x)) + re(x))*(-pi + i*(im(x) + im(asin(1/10 + 3*x/2))) + re(x) + re(asin(1/10 + 3*x/2)))
Rapid solution
[src]
/ / /1 3*x\\\ / /1 3*x\\
y1 = -re(x) + I*|-im(x) + im|asin|-- + ---||| + re|asin|-- + ---||
\ \ \10 2 /// \ \10 2 //
$$y_{1} = i \left(- \operatorname{im}{\left(x\right)} + \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}$$
/ /1 3*x\\ / / /1 3*x\\\
y2 = pi - re(x) - re|asin|-- + ---|| + I*|-im(x) - im|asin|-- + ---|||
\ \10 2 // \ \ \10 2 ///
$$y_{2} = i \left(- \operatorname{im}{\left(x\right)} - \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)}\right) - \operatorname{re}{\left(x\right)} - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3 x}{2} + \frac{1}{10} \right)}\right)} + \pi$$
y2 = i*(-im(x) - im(asin(3*x/2 + 1/10))) - re(x) - re(asin(3*x/2 + 1/10)) + pi