Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 8-3/5x=17
-
Equation x^2=-100
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Equation 3*x-7/8-x-3/6=1
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Equation cos(x)=pi/2
- Express {x} in terms of y where:
- 1*x+18*y=-5
- 18*x-7*y=-4
- -15*x+9*y=-6
- -13*x-12*y=-11
- Derivative of:
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cos(x)
- pi/2
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
- pi/2
- Limit of the function:
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pi/2
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Identical expressions
- cos(x)=pi/ two
- co sinus of e of (x) equally Pi divide by 2
- co sinus of e of (x) equally Pi divide by two
- cosx=pi/2
- cos(x)=pi divide by 2
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Similar expressions
- sqrt(38)*cos(x/2+3pi/4)=sqrt(37-sin(3x))
- cosx=pi/2
cos(x)=pi/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \frac{\pi}{2}$$
- 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.
$$\cos{\left(x \right)} = \frac{\pi}{2}$$
- 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]
/ /pi\\
x1 = 2*pi - I*im|acos|--||
\ \2 //
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}$$
/ /pi\\ / /pi\\
x2 = I*im|acos|--|| + re|acos|--||
\ \2 // \ \2 //
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}$$
x2 = re(acos(pi/2)) + i*im(acos(pi/2))
Sum and product of roots
[src]
sum
/ /pi\\ / /pi\\ / /pi\\
2*pi - I*im|acos|--|| + I*im|acos|--|| + re|acos|--||
\ \2 // \ \2 // \ \2 //
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right)$$
=
/ /pi\\
2*pi + re|acos|--||
\ \2 //
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)} + 2 \pi$$
product
/ / /pi\\\ / / /pi\\ / /pi\\\ |2*pi - I*im|acos|--|||*|I*im|acos|--|| + re|acos|--||| \ \ \2 /// \ \ \2 // \ \2 ///
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right)$$
=
/ / /pi\\\ / / /pi\\ / /pi\\\ |2*pi - I*im|acos|--|||*|I*im|acos|--|| + re|acos|--||| \ \ \2 /// \ \ \2 // \ \2 ///
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{\pi}{2} \right)}\right)}\right)$$
(2*pi - i*im(acos(pi/2)))*(i*im(acos(pi/2)) + re(acos(pi/2)))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.02322747854755*i
x2 = 1.02322747854755*i
x2 = 1.02322747854755*i
The graph