Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)=2
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Equation tan(x)=-1
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Equation sin(pi*x)=1
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Equation 1-2*(5-2*x)=-x-3
- Express {x} in terms of y where:
- -10*x-16*y=-6
- -13*x+9*y=1
- 4*x+3*y=-15
- -2*x+1*y=-8
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)= two
- co sinus of e of (x) equally 2
- co sinus of e of (x) equally two
- cosx=2
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Similar expressions
- sinx/1+cosx=1-cosx
- cosx=3^0.5/2
- sinx*cospi/8+cosx*sinpi/8=1/2
- cosx=2
cos(x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = 2$$
- this is the simplest trigonometric equation
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.
$$\cos{\left(x \right)} = 2$$
- this is the simplest trigonometric equation
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 = 2*pi - I*im(acos(2))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}$$
x2 = I*im(acos(2)) + re(acos(2))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}$$
Sum and product of roots
[src]
sum
0 + 2*pi - I*im(acos(2)) + I*im(acos(2)) + re(acos(2))
$$\left(0 + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)$$
=
2*pi + re(acos(2))
$$\operatorname{re}{\left(\operatorname{acos}{\left(2 \right)}\right)} + 2 \pi$$
product
1*(2*pi - I*im(acos(2)))*(I*im(acos(2)) + re(acos(2)))
$$1 \cdot \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)$$
=
(2*pi - I*im(acos(2)))*(I*im(acos(2)) + re(acos(2)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(2 \right)}\right)}\right)$$
(2*pi - i*im(acos(2)))*(i*im(acos(2)) + re(acos(2)))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.31695789692482*i
x2 = 1.31695789692482*i
x2 = 1.31695789692482*i
The graph