Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation a^2*x^2-21*a^2+a*x+1=0
-
Equation -(-y+4)+2*y+1=0
-
Equation 3^x=8
-
Equation 5*cos(x)=6
- Express {x} in terms of y where:
- -16*x-20*y=-13
- 12*x-14*y=5
- -19*x-2*y=2
- -20*x-4*y=-14
- Graphing y =:
- 5*cos(x)
- Derivative of:
-
5*cos(x)
-
Identical expressions
- five *cos(x)= six
- 5 multiply by co sinus of e of (x) equally 6
- five multiply by co sinus of e of (x) equally six
- 5cos(x)=6
- 5cosx=6
-
Similar expressions
- 6sinx+15cosx=√261
- 2*log((11/5)*cos(x))-9*log((11/5)*cos(x))+4=0
- sin(x/3)+5cos(x/3)=0
- 5*cosx=6
5*cos(x)=6 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$5 \cos{\left(x \right)} = 6$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = \frac{6}{5}$$
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.
$$5 \cos{\left(x \right)} = 6$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 5
The equation is transformed to
$$\cos{\left(x \right)} = \frac{6}{5}$$
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(6/5))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}$$
x2 = I*im(acos(6/5)) + re(acos(6/5))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}$$
x2 = re(acos(6/5)) + i*im(acos(6/5))
Sum and product of roots
[src]
sum
2*pi - I*im(acos(6/5)) + I*im(acos(6/5)) + re(acos(6/5))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right)$$
=
2*pi + re(acos(6/5))
$$\operatorname{re}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)} + 2 \pi$$
product
(2*pi - I*im(acos(6/5)))*(I*im(acos(6/5)) + re(acos(6/5)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right)$$
=
(2*pi - I*im(acos(6/5)))*(I*im(acos(6/5)) + re(acos(6/5)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{6}{5} \right)}\right)}\right)$$
(2*pi - i*im(acos(6/5)))*(i*im(acos(6/5)) + re(acos(6/5)))
Numerical answer
[src]
x1 = 6.28318530717959 - 0.622362503714779*i
x2 = 0.622362503714779*i
x2 = 0.622362503714779*i
The graph