Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2+6*x+16=0
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Equation sqrt(x+3)=x-3
- Equation x-y=5
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Equation cos(x)=1/4
- Express {x} in terms of y where:
- -6*x+12*y=11
- -13*x-7*y=16
- 5*x+19*y=-3
- 15*x+10*y=-4
- Sum of series:
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-1
- Integral of d{x}:
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-1
- Derivative of:
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-1
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Identical expressions
- cosx/ seven =- one
- co sinus of e of x divide by 7 equally minus 1
- co sinus of e of x divide by seven equally minus one
- cosx divide by 7=-1
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Similar expressions
- cos(x/7)=-sqrt(3)/2
- cosx/7=+1
- sin^2((180-x)/(4k+2))-(1-cos(x))/72=0
- (85*cos(x)^(2)+77*cos(x))/77*tan(x)-36=0
cosx/7=-1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{7} = -1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = -7$$
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.
$$\frac{\cos{\left(x \right)}}{7} = -1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/7
The equation is transformed to
$$\cos{\left(x \right)} = -7$$
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 = -re(acos(-7)) + 2*pi - I*im(acos(-7))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}$$
x2 = I*im(acos(-7)) + re(acos(-7))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}$$
x2 = re(acos(-7)) + i*im(acos(-7))
Sum and product of roots
[src]
sum
-re(acos(-7)) + 2*pi - I*im(acos(-7)) + I*im(acos(-7)) + re(acos(-7))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
(-re(acos(-7)) + 2*pi - I*im(acos(-7)))*(I*im(acos(-7)) + re(acos(-7)))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right)$$
=
-(I*im(acos(-7)) + re(acos(-7)))*(-2*pi + I*im(acos(-7)) + re(acos(-7)))
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-7 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-7 \right)}\right)}\right)$$
-(i*im(acos(-7)) + re(acos(-7)))*(-2*pi + i*im(acos(-7)) + re(acos(-7)))
Numerical answer
[src]
x1 = 3.14159265358979 + 2.63391579384963*i
x2 = 3.14159265358979 - 2.63391579384963*i
x2 = 3.14159265358979 - 2.63391579384963*i