Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation 6sin^2x+sin2x=2
- Equation cos(pi(x+1))/2=-1
-
Equation cos(x+pi/3)=0
-
Equation sin(3*x-pi/4)=sqrt(3)/2
- Express {x} in terms of y where:
- 15*x+15*y=16
- -4*x+18*y=-14
- 8*x+7*y=-13
- -12*x+3*y=-9
- Sum of series:
-
-1
- Derivative of:
-
-1
- Integral of d{x}:
-
-1
-
Identical expressions
- cos(pi(x+ one))/ two =- one
- co sinus of e of ( Pi (x plus 1)) divide by 2 equally minus 1
- co sinus of e of ( Pi (x plus one)) divide by two equally minus one
- cospix+1/2=-1
- cos(pi(x+1)) divide by 2=-1
-
Similar expressions
- (cos)pi(x+1)/2=-1
- cos(pi(x+1))/2=+1
- cos(pi(x-1))/2=-1
cos(pi(x+1))/2=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
cos(pi*(x + 1))
--------------- = -1
2
$$\frac{\cos{\left(\pi \left(x + 1\right) \right)}}{2} = -1$$
Detail solution
Given the equation
$$\frac{\cos{\left(\pi \left(x + 1\right) \right)}}{2} = -1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(\pi x \right)} = 2$$
As right part of the equation
modulo =
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\frac{\cos{\left(\pi \left(x + 1\right) \right)}}{2} = -1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1/2
The equation is transformed to
$$\cos{\left(\pi x \right)} = 2$$
As right part of the equation
modulo =
True
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
Rapid solution
[src]
I*im(acos(2))
x1 = -------------
pi
$$x_{1} = \frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi}$$
I*im(acos(2))
x2 = 2 - -------------
pi
$$x_{2} = 2 - \frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi}$$
x2 = 2 - i*im(acos(2))/pi
Sum and product of roots
[src]
sum
I*im(acos(2)) I*im(acos(2))
------------- + 2 - -------------
pi pi
$$\left(2 - \frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi}\right) + \frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi}$$
=
2
$$2$$
product
I*im(acos(2)) / I*im(acos(2))\
-------------*|2 - -------------|
pi \ pi /
$$\frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi} \left(2 - \frac{i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi}\right)$$
=
(2*pi*I + im(acos(2)))*im(acos(2))
----------------------------------
2
pi
$$\frac{\left(\operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)} + 2 i \pi\right) \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}}{\pi^{2}}$$
(2*pi*i + im(acos(2)))*im(acos(2))/pi^2
Numerical answer
[src]
x1 = 0.419200718278983*i
x2 = 2.0 - 0.419200718278983*i
x2 = 2.0 - 0.419200718278983*i