Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+12=5
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Equation 3/(x-5)+8/x=2
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Equation (5x-2)*(-x+3)=0
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Equation 1-x/2=x/3
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- 12*x+1*y=15
- Graphing y =:
- cos(x)/3
- Derivative of:
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cos(x)/3
- Integral of d{x}:
- cos(x)/3
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Identical expressions
- cos(x)/ three = one
- co sinus of e of (x) divide by 3 equally 1
- co sinus of e of (x) divide by three equally one
- cosx/3=1
- cos(x) divide by 3=1
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Similar expressions
- cos(x/3)=-1/2
- cosx/3=sqrt(x-1)
- cos(x/3+pi/4)=1/2
- -1/3*cos(x/3+pi/4)-cos=sin(x)
- cosx/3=1
cos(x)/3=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{3} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = 3$$
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.
$$\frac{\cos{\left(x \right)}}{3} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\cos{\left(x \right)} = 3$$
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.
Sum and product of roots
[src]
sum
2*pi - I*im(acos(3)) + I*im(acos(3)) + re(acos(3))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
=
2*pi + re(acos(3))
$$\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + 2 \pi$$
product
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
=
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
(2*pi - i*im(acos(3)))*(i*im(acos(3)) + re(acos(3)))
Rapid solution
[src]
x1 = 2*pi - I*im(acos(3))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}$$
x2 = I*im(acos(3)) + re(acos(3))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}$$
x2 = re(acos(3)) + i*im(acos(3))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.76274717403909*i
x2 = 1.76274717403909*i
x2 = 1.76274717403909*i
The graph