Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x*8=25+15
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Equation cos(x)=5
- Equation (x-4)^4-4*(x-4)^2-21=0
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Equation ((1/5))^(x)^(2)*5^(2*x+2)=(1/5)^(6)
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 15*x+7*y=2
- 12*x-20*y=10
- -11*x-1*y=15
- 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)= five
- co sinus of e of (x) equally 5
- co sinus of e of (x) equally five
- cosx=5
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Similar expressions
- cos(x+(pi/6))=1
- cosx=5
cos(x)=5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = 5$$
- 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.
$$\cos{\left(x \right)} = 5$$
- 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.
Sum and product of roots
[src]
sum
0 + 2*pi - I*im(acos(5)) + I*im(acos(5)) + re(acos(5))
$$\left(0 + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
=
2*pi + re(acos(5))
$$\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + 2 \pi$$
product
1*(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
$$1 \cdot \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
=
(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
(2*pi - i*im(acos(5)))*(i*im(acos(5)) + re(acos(5)))
Rapid solution
[src]
x1 = 2*pi - I*im(acos(5))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}$$
x2 = I*im(acos(5)) + re(acos(5))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}$$
Numerical answer
[src]
x1 = 6.28318530717959 - 2.29243166956118*i
x2 = 2.29243166956118*i
x2 = 2.29243166956118*i
The graph