Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1-5*x=-6*x+8
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Equation 3-3*6+2=x
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Equation x^2=-25
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Equation cos(x/2)=-(1/2)
- Express {x} in terms of y where:
- 4*x-7*y=4
- 8*x+3*y=4
- 11*x-19*y=14
- 4*x-3*y=-15
- Derivative of:
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cos(x)/5
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-1
- Graphing y =:
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cos(x)/5
- Sum of series:
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-1
- Integral of d{x}:
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-1
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Identical expressions
- cos(x)/ five =- one
- co sinus of e of (x) divide by 5 equally minus 1
- co sinus of e of (x) divide by five equally minus one
- cosx/5=-1
- cos(x) divide by 5=-1
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Similar expressions
- cos(x/2)=-(1/2)
- 2cos(x/5)=5
- cos(x)/5=+1
- sqrt(cos(x)^2-cos(x))/5-1=0
- cosx/5=-1
cos(x)/5=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{5} = -1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = -5$$
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.
$$\frac{\cos{\left(x \right)}}{5} = -1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5
The equation is transformed to
$$\cos{\left(x \right)} = -5$$
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]
x1 = -re(acos(-5)) + 2*pi - I*im(acos(-5))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}$$
x2 = I*im(acos(-5)) + re(acos(-5))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}$$
Sum and product of roots
[src]
sum
0 + -re(acos(-5)) + 2*pi - I*im(acos(-5)) + I*im(acos(-5)) + re(acos(-5))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
1*(-re(acos(-5)) + 2*pi - I*im(acos(-5)))*(I*im(acos(-5)) + re(acos(-5)))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right)$$
=
-(I*im(acos(-5)) + re(acos(-5)))*(-2*pi + I*im(acos(-5)) + re(acos(-5)))
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right)$$
-(i*im(acos(-5)) + re(acos(-5)))*(-2*pi + i*im(acos(-5)) + re(acos(-5)))
Numerical answer
[src]
x1 = 3.14159265358979 + 2.29243166956118*i
x2 = 3.14159265358979 - 2.29243166956118*i
x2 = 3.14159265358979 - 2.29243166956118*i
The graph