Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -20*(x-13)=-220
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Equation x-x/12=55/12
-
Equation 3^x=81
-
Equation 12-x^2=11
- Express {x} in terms of y where:
- 18*x+19*y=7
- 1*x+6*y=6
- 20*x+9*y=17
- 11*x-11*y=-17
- Derivative of:
- cosx/5
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1/2
- Sum of series:
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1/2
- Integral of d{x}:
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1/2
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Identical expressions
- cosx/ five = one / two
- co sinus of e of x divide by 5 equally 1 divide by 2
- co sinus of e of x divide by five equally one divide by two
- cosx divide by 5=1 divide by 2
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Similar expressions
- cos(x/5)=-(\sqrt(3))/(2)
- 2*cos(x/5)+cos(2*x/5)-2*cos(4*x/5)-cos(7*x/5)-cos(x)+cos(2*x)=0
cosx/5=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{5} = \frac{1}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = \frac{5}{2}$$
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.
$$\frac{\cos{\left(x \right)}}{5} = \frac{1}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5
The equation is transformed to
$$\cos{\left(x \right)} = \frac{5}{2}$$
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(5/2))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}$$
x2 = I*im(acos(5/2)) + re(acos(5/2))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}$$
x2 = re(acos(5/2)) + i*im(acos(5/2))
Sum and product of roots
[src]
sum
2*pi - I*im(acos(5/2)) + I*im(acos(5/2)) + re(acos(5/2))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right)$$
=
2*pi + re(acos(5/2))
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + 2 \pi$$
product
(2*pi - I*im(acos(5/2)))*(I*im(acos(5/2)) + re(acos(5/2)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right)$$
=
(2*pi - I*im(acos(5/2)))*(I*im(acos(5/2)) + re(acos(5/2)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right)$$
(2*pi - i*im(acos(5/2)))*(i*im(acos(5/2)) + re(acos(5/2)))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.56679923697241*i
x2 = 1.56679923697241*i
x2 = 1.56679923697241*i