Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=3
-
Equation -3x-9=2x
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Equation x/4+x=4
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Equation (-x-4)(3x+3)=0
- Express {x} in terms of y where:
- 16*x-17*y=-9
- 4*x+16*y=6
- -19*x+1*y=0
- 20*x+13*y=1
- Derivative of:
- cosx/5
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Identical expressions
- cosx/ five =-(√ three / two)
- co sinus of e of x divide by 5 equally minus (√3 divide by 2)
- co sinus of e of x divide by five equally minus (√ three divide by two)
- cosx/5=-√3/2
- cosx divide by 5=-(√3 divide by 2)
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Similar expressions
- 2cos(x/5)=5
- -822*sin(x)/(5*(26*cos(x)/125+489*sin(x)/500))+822*(-489*cos(x)/500+26*sin(x)/125)*cos(x)/(5*(26*cos(x)/125+489*sin(x)/500)^2)=0
- cos(x)=(-√3/2)
- cosx/5=+(√3/2)
- cos(-2x)=-√3/2
- cos(x)/5=-1
- -cosx/3-√3/2/3=0
- 2*cos(x/5)+cos(2*x/5)-2*cos(4*x/5)-cos(7*x/5)-cos(x)+cos(2*x)=0
- cos(2x-pi/4)=-√3/2
cosx/5=-(√3/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ cos(x) -\/ 3 ------ = ------- 5 2
$$\frac{\cos{\left(x \right)}}{5} = - \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{5} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = - \frac{5 \sqrt{3}}{2}$$
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.
$$\frac{\cos{\left(x \right)}}{5} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5
The equation is transformed to
$$\cos{\left(x \right)} = - \frac{5 \sqrt{3}}{2}$$
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.
Sum and product of roots
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |-5*\/ 3 || | |-5*\/ 3 || | |-5*\/ 3 || | |-5*\/ 3 ||
- re|acos|--------|| + 2*pi - I*im|acos|--------|| + I*im|acos|--------|| + re|acos|--------||
\ \ 2 // \ \ 2 // \ \ 2 // \ \ 2 //
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ | | |-5*\/ 3 || | |-5*\/ 3 ||| | | |-5*\/ 3 || | |-5*\/ 3 ||| |- re|acos|--------|| + 2*pi - I*im|acos|--------|||*|I*im|acos|--------|| + re|acos|--------||| \ \ \ 2 // \ \ 2 /// \ \ \ 2 // \ \ 2 ///
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ | | |-5*\/ 3 || | |-5*\/ 3 ||| | | |-5*\/ 3 || | |-5*\/ 3 ||| -|I*im|acos|--------|| + re|acos|--------|||*|-2*pi + I*im|acos|--------|| + re|acos|--------||| \ \ \ 2 // \ \ 2 /// \ \ \ 2 // \ \ 2 ///
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right)$$
-(i*im(acos(-5*sqrt(3)/2)) + re(acos(-5*sqrt(3)/2)))*(-2*pi + i*im(acos(-5*sqrt(3)/2)) + re(acos(-5*sqrt(3)/2)))
Rapid solution
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/ / ___\\ / / ___\\
| |-5*\/ 3 || | |-5*\/ 3 ||
x1 = - re|acos|--------|| + 2*pi - I*im|acos|--------||
\ \ 2 // \ \ 2 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}$$
/ / ___\\ / / ___\\
| |-5*\/ 3 || | |-5*\/ 3 ||
x2 = I*im|acos|--------|| + re|acos|--------||
\ \ 2 // \ \ 2 //
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}$$
x2 = re(acos(-5*sqrt(3)/2)) + i*im(acos(-5*sqrt(3)/2))
Numerical answer
[src]
x1 = 3.14159265358979 + 2.14513586791928*i
x2 = 3.14159265358979 - 2.14513586791928*i
x2 = 3.14159265358979 - 2.14513586791928*i