Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=1/5
-
Equation x^2+11=0
-
Equation x^2+5x+6=0
-
Equation -x/7+x=15/7
- Express {x} in terms of y where:
- 9*x+17*y=13
- 20*x+18*y=-9
- -4*x-8*y=-20
- -1*x+4*y=-10
-
Identical expressions
- sin(pi*x)/ three = one
- sinus of ( Pi multiply by x) divide by 3 equally 1
- sinus of ( Pi multiply by x) divide by three equally one
- sin(pix)/3=1
- sinpix/3=1
- sin(pi*x) divide by 3=1
-
Similar expressions
- sin(pi*x/3)=1/2
sin(pi*x)/3=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\sin{\left(\pi x \right)}}{3} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\pi x \right)} = 3$$
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.
$$\frac{\sin{\left(\pi x \right)}}{3} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\sin{\left(\pi x \right)} = 3$$
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)) I*im(asin(3)) re(asin(3)) I*im(asin(3))
0 + ---------------- - ------------- + ----------- + -------------
pi pi pi pi
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}\right) + \left(0 + \left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}\right)\right)$$
=
pi - re(asin(3)) re(asin(3))
---------------- + -----------
pi pi
$$\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}$$
product
/pi - re(asin(3)) I*im(asin(3))\ /re(asin(3)) I*im(asin(3))\ 1*|---------------- - -------------|*|----------- + -------------| \ pi pi / \ pi pi /
$$1 \left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}\right) \left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}\right)$$
=
(I*im(asin(3)) + re(asin(3)))*(pi - re(asin(3)) - I*im(asin(3)))
----------------------------------------------------------------
2
pi
$$\frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)}{\pi^{2}}$$
(i*im(asin(3)) + re(asin(3)))*(pi - re(asin(3)) - i*im(asin(3)))/pi^2
Rapid solution
[src]
pi - re(asin(3)) I*im(asin(3))
x1 = ---------------- - -------------
pi pi
$$x_{1} = \frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}$$
re(asin(3)) I*im(asin(3))
x2 = ----------- + -------------
pi pi
$$x_{2} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}}{\pi}$$
Numerical answer
[src]
x1 = 0.5 + 0.56109985233918*i
x2 = 0.5 - 0.56109985233918*i
x2 = 0.5 - 0.56109985233918*i
The graph