Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-4)^2+(x+9)^2=2*x^2
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Equation 9-2(-4x+7)=7
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Equation sin(x)+1/2=0
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Equation 4^x-12*2^x+32=0
- Express {x} in terms of y where:
- -11*x+4*y=-8
- -14*x+1*y=3
- 14*x+16*y=14
- 16*x+7*y=8
- Integral of d{x}:
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cosx
- Derivative of:
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cosx
- Graphing y =:
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cosx
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Identical expressions
- cosx=- one . two
- co sinus of e of x equally minus 1.2
- co sinus of e of x equally minus one . two
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Similar expressions
- cos(x)=1/3
- (1.25(x+1)((2/x)+(((1.25^2)-1)/x^2)^0.5)-((1.25^2)-1))/(1+((1.25^2)/x^2))-20=0
- cos(x)=sin(x)
- 9,05*((1,232^2)*(arccos((1,232-x)/1,232))-(1.232-x)*((2*1.232-x)^(1/2)))=37.881
- cosx=+1.2
cosx=-1.2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = - \frac{6}{5}$$
- 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.
$$\cos{\left(x \right)} = - \frac{6}{5}$$
- 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 + -re(acos(-6/5)) + 2*pi - I*im(acos(-6/5)) + I*im(acos(-6/5)) + re(acos(-6/5))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
1*(-re(acos(-6/5)) + 2*pi - I*im(acos(-6/5)))*(I*im(acos(-6/5)) + re(acos(-6/5)))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right)$$
=
-(I*im(acos(-6/5)) + re(acos(-6/5)))*(-2*pi + I*im(acos(-6/5)) + re(acos(-6/5)))
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}\right)$$
-(i*im(acos(-6/5)) + re(acos(-6/5)))*(-2*pi + i*im(acos(-6/5)) + re(acos(-6/5)))
Rapid solution
[src]
x1 = -re(acos(-6/5)) + 2*pi - I*im(acos(-6/5))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}$$
x2 = I*im(acos(-6/5)) + re(acos(-6/5))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{6}{5} \right)}\right)}$$
Numerical answer
[src]
x1 = 3.14159265358979 + 0.622362503714779*i
x2 = 3.14159265358979 - 0.622362503714779*i
x2 = 3.14159265358979 - 0.622362503714779*i
The graph